UNIVERSITA DEGLI STUDI DI MILANO-BICOCCA

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1 UNIVERSITA DEGLI STUDI DI MILANO-BICOCCA SCUOLA DI DOTTORATO DI SCIENZE CORSO DI DOTTORATO DI RICERCA IN FISICA E ASTRONOMIA XXI CICLO Neutron spectroscopy for diagnostics on JET fusion plasma Supervisor: Prof. Giuseppe Gorini Coordinator of the PhD School: Prof. Claudio Destri PhD Dissertation by Flora Ognissanto Matr PACS xxxx xx May 2009

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3 Abstract The Neutron Emission Spectroscopy (NES) is an effective diagnostic method for investigating fusion plasmas: it provides information about the plasma parameters working without perturbing the plasma. The subject of this thesis is the neutron spectroscopy applied to fusion plasmas confined in Tokamak devices with particular reference to the Joint European Torus (JET) and the International Thermonuclear Experimental Reactor (ITER). The considered plasma are constituted by deuterium ions or by a mixture 50:50 of deuterium and tritium; the main reactions involved in the neutron emission are d+d 3 He+n and d+t α+n. The neutron yield and energy spread depends on the reactants temperature and density profiles; these are not uniform in Tokamaks so that the features of the revealed neutron spectrum depend on the volume portion intersected by the spectrometer sight line (SL). The SL influence on the neutron spectrum was investigated through analytical and numerical calculations. Based on the Monte Carlo method, neutron spectrum simulations were performed for thermal plasmas considering the SL of the two spectrometers working at JET, MPR and TOFOR. The thermal spectrum has a Gaussian shape whose full width at half maximum gives the effective temperature T eff of the reactant ions. Through this study it is observed the relationship between the T eff of the two instruments for different plasma profiles and the benefit of having two distinct SL emerged. Comparing the obtained values it is found that the TOFOR SL reveals temperatures higher than MPR. This peculiarity gave rise to an analytical study of T eff as function of parametrized SLs which clarified what observed. At JET a special feature of MPR was found: the neutron yield deducible from the neutron flux it measures, F n, is proportional to the total neutron yield, Y n. To justify this observation, analytical calculations of the proportional coefficient between F n and Y n were performed for different parametrized SLs and plasma profiles. A SL with weak plasma parameters dependence was individuated: this explains the particularity pointed out for the MPR SL. This study underlines the potentiality of NES as means to know the total neutron yield: characteristic of particular relevance for the designing of the future fusion project, ITER. The possibility of discriminating the spectral components for ITER plasmas was investigated performing simulations. Different plasma scenarios were examined

4 changing the ions mixtures and heating and two SLs were considered. This study describes what we can obtain from a spectrum emitted by such plasmas and it puts in evidence the advisable characteristic for an ITER spectrometer. During experiments at JET in January 2007 high energy tails in the neutron spectra were observed and it was supposed they were originated by the 3 He knock-on neutron emission. In accordance to this mechanism the radio frequency heating tuned to 3 He is able to produce high energy tails in the 3 He distribution function and these ions can transfer a big amount of their energy to bulk deuterons by means of scattering at large angles, giving rise to a suprathermal deuteron population. From the fusion reactions between this suprathermal deuteron population and thermal bulk deuterons high energy neutrons are produced, i.e. the 3 He knock-on component, HKN. In order to simulate the process, the deuteron- 3 He scattering cross section is needed: it is not available from theory so that it was necessary a survey of the existing experimental data. Subsequently it was carried on an interpolation and extrapolation of the data to unmeasured regions based on phenomenological considerations and, when suitable, calculated Coulomb cross sections. Comparing simulations obtained with the empirical or the pure Coulombian cross sections it has been possible to evaluate the importance of the nuclear interaction in the scattering process. From this study was possible to compare the HKN contribution to the spectrum in comparison to components due to other processes taking place in the plasma. The simulations performed were in good agreement with the JET observations so that the model was convalidated.

5 Contents 1 Nuclear fusion Introduction Fusion reactions Physics process Ignition Reactions of interest for the development of the controlled thermonuclear fusion JET experiment Radio frequency heating Neutral Beam Injection heating ITER Heating in ITER Neutron diagnostics and neutron emission spectroscopy (NES) The MPR spectrometer The TOFOR spectrometer Neutron flux diagnostic at JET Neutron diagnostic at ITER Neutron emissions Fusion neutron kinematics Emission processes Thermal emission The AKN and HKN emissions TBN Monte Carlo simulations III

6 3 Sight line effects Thermal neutron spectrum: local and observed Thermal neutron spectrum: simulations Simulated thermal neutron spectrum: results Analytical calculation Results of the analytical calculations SL effects on absolute neutron yield SL considerations on ITER He Knock-on High energy neutron spectrum in presence of 3 He: HKN process Classical kinematics of a scattering event He(d, 3 He)d Scattering Cross Sections Simulations Influence of the scattering cross sections uncertainties on the neutron spectrum Simulation and measurement comparison Scattering cross sections: Coulomb or nuclear? Conclusions Bibliography Synopsis P1 Line integration effects on ion temperatures in tokamak plasmas measured with neutron emission spectroscopy IV

7 P2 Relationship between neutron yield rate of tokamak plasmas and spectrometer measured flux for different sight lines P2 Diagnostic information from non thermal neutron emission on ITER P3 Nuclear scattering effects on the neutron emission in fusion plasmas P4 Τhe elastic 3 He+d cross section of relevance for knock-on effects in d+d fusion reactions in RF heated deuterium plasmas Acknowledgments V

8 VI

9 1 Nuclear fusion 1.1 Introduction The demand of energy in our society is continuously increasing because of the growth of emerging economies and of the world population. Indeed, the fossil fuels may be exhausted in the next years with an increase of costs and of the environmental impact. Thus emerges the necessity of developing a new energy source to rely on. As a matter of fact, renewable sources, even playing an important role, could be not enough. Nuclear fission while reducing the dependence on fossil fuels and the production of greenhouse gases on one hand, poses problems connected to the radioactive waste storage, safety and nuclear material proliferation on the other hand. We can summarize by saying that we need sustainable energy, available on large-scale and for the long term period. Nuclear fusion may fulfill all these requirements. First of all the fuel is almost inexhaustible. The fuel nuclei are deuterium and tritium (d, t), the first is extracted from the water, which implies that it would last millions of years, while material providing tritium is lithium, which is an abundant metal on Earth. One possible reaction generating tritium is n+ 6 Li t+α+q, with Q=4.8 MeV, or n+ 7 Li t+α+n+q, Q=-2.5 MeV. These reactions can be realized in a fusion reactor, where the produced neutrons may react with a certain quantity of lithium put in the wall of the vessel. The amount of d and t in the reaction chamber is very small, just a few grams in a volume of about 1000 cubic metres. In order to allow self sustained fusion reactions, temperature and density may fulfill stringent and controllable conditions thus making fusion a safe process. As a matter of fact, the neutrons produced in the fusion reactions may activate the surrounding materials, so that the selection of low activation materials is a key feature for the construction of power station. Another benefit from thermonuclear fusion is its low environmental impact, as both greenhouse gases and pollutants are not generated. 1

10 1.2 Fusion reactions The energy production from thermonuclear fusion is based on the mass defect between the reactants and the product nuclei. Looking at light nuclides we note that there is a large difference in the binding energy, in particular the lighter is the nucleus the higher is the binding energy. This implies that products with smaller binding energies are created from the fusion of these nuclides with a net energy output released as kinetic energy of the reaction products. In tab. 1.1 the main fusion reaction between light nuclides are shown. In order to speed up fusion technology in 1970 the Council of the European Community decided for a forefront fusion programme and provided the necessary legal framework for the development of an European fusion device. Three years later at Culham (UK), the design work began for the JET device whose construction ended in 1983 ( 1.2). JET has achieved a ratio of fusion power input close to unity. The next step for fusion is the construction of of ITER ( 1.3), a collaboration among the European Union, India, Japan, the Republic of Korea, China, the Russian Federation and the United States of America. The site of the experiment is Cadarache (France), where works of construction started in 2007 and the first plasma is planned for ITER will be the first fusion experiment to achieve a net gain in energy with an expected Q factor exceeding Physics process In order for nuclear fusion to take place the distance between the fusing nuclei must be of the order of the nuclear dimension itself. The Coulomb repulsion can only be overcome by the tunneling effect. Thus the fusion cross section is proportional to the tunnelling probability σ 2πZ Z e 1 2 hν ( ν ) e 2 (1.1) where ν is the relative velocity of the reacting particles [1]. Parametrizations of the fusion cross section have been developed and made more accurate 2

11 Reaction Products and relative energies in MeV 1a 50% d + d t(1.011) + p(3.022) 1b 50% 1c 10-5 % 2 p + t 3 He(0.820) + n(2.499) 4 He + γ(23.8) 3 He + n p + d 4a t + d 4b % 5 t + t 6a d + 3 He 6b % 7a 51% t + 3 He 7b 43% 7c 6% 3 He + γ(5.5) 4 He (3.561) + n(14.029) 5 He + γ(16.6) 4 He + 2n He(3.712) + p(14.641) 5 Li + γ(16.5) 4 He + n + p He(4.800) + d(9.520) 4 He(0.5) + n(1.9)+p(11.9) 8 3 He + 3 He 4 He + 2p d + 6 Li 2 4 He p + 6 Li 4 He(1.7) + 3 He(2.3) 11 3 He + 6 Li 2 4 He + p p + 11 B 3 4 He Tab. 1.1: Main fusion reactions for light nuclei. When the reaction includes different branches, the percentages are shown. For each reaction the average kinetic energy of the products is indicated. When the reaction generates three particles the energy released is added separately. 3

12 over the years [2]. From the ions distribution functions f 1 (v 1 ), f 2 (v 2 ) and the relative velocity v, we obtain the fusion reaction rate by integrating 3 3 R = 2 σ ( v) v f1 ( v1) f 2 ( v 2 ) d v1d v (1.2) 2 For a given σ parametrization we can write more conveniently the reaction rate asr = n 1 n2 < σv > T, where n 1, n 2 are the ion densities and the reactivity <σv> T depends on the plasma temperature T. In the case of a DT plasma, the maximum rate for a certain ion density is achieved for n D =n T. In this condition, the thermonuclear power per unit of volume p=n D (n-n D ) <σv> T Ē (being Ē the energy released per reaction)is also maximized and can be written as p= ¼ n 2 <σv> T Ē. In fig. 1.1, the reactivity for dt and dd reactions as function of the temperature from 10 to 100 kev is plotted in accordance with the parametrization used by Peres [3]. From the point of view of the reaction rate, the dt process results more favourable since the rate is higher of about two orders of magnitude with respect to dd case. If we analysed the rate for the d 3 He reactions, we found that it is much smaller that that for dt but it is a process of interest if compared with dd fusion for temperatures over 25 kev where <σv> T overcomes the value of the former [4] dt dd T [kev] Fig. 1.1: Thermonuclear reaction rate for dd and dt reactions as function of ion temperature. The numerical parameters for the calculation are from [3]. 4

13 1.2.2 Ignition Bearing in mind the purpose of having a net gain of energy from the fusion process, we calculate the amount of power applied and obtained so to find out the required conditions of temperature, density and confinement time. To keep the plasma on, it is necessary supply the energy losses by providing external power P H, so that in the steady state we have P H =P L, where P L = W / τ is the power loss being W the energy of the plasma and the time τ E of its confinement. The average energy for unit of volume in a neutral plasma at temperature T is given by the sum of ½nT for degree of freedom, for both ions and E 3 electrons, so that the total energy is W = 3nTd x = 3nTV, where the bar indicates the average value. Obviously this situation has no energetic advantage, but we can study a way to profit by the plasma itself for keeping it hot enough to let the fusion processes go on. The α particles produced in the dt interactions are used for this purpose. In this process one neutron and one α are generated: the ion remains trapped in the magnetic field and so its 3.5 MeV kinetic energy can be transferred to the fuel ions through collisions. The thermonuclear power per unit of volume is p=n D (n-n D )<σv> T Ē (see previous paragraph) so we obtain for the total α particle induced heating P α 1 2 = n σv EαV. In this condition the plasma 4 have two sources of power, an external one, P H, and that due to the α, so the balance is P H +P α =P L, that is P H 1 3nT + n 2 σv EαV = V (1.3) 4 τ The goal is to achieve the condition in which only α particles can sustain the plasma, with no further external power apart from the starting stage, i.e. the ignition. From equation (1.3) we have P E 3nT 1 2 = ( n < σv > Eα V where the τ 4 H ) E density and temperature are taken as constant for simplicity. The requirement of 3nT 1 2 ignition is therefore n < σv > Eα < 0. This leads to τ 4 E 5

14 T nτ E > 12 (1.4) < σv > E The right hand side is a function of the temperature only and it has a minimum at T~30keV, corresponding to nτ E > m -3 s. Actually the T required results to be somewhat lower and this is due to the dependence of τ E from the temperature. In the range of interest, kev, the reaction rate can be parametrized, with an accurancy of the 10%, as <σv>= T 2 m 3 s -1 where the temperature is in kev. Considering that E α =3.5 MeV, the ignition condition becomes ntτ E > m -3 kev s (1.5) The constant depends on the profiles of n and T and if we are considering average or peak values. The value above refers to flat profiles, while, for instance, in the case of parabolic profiles it is m -3 kevs on the peak value. This criterion shows how temperature, ion density and confinement time are bounded each other to achieve the ignition. In fig. 1.2 the performance recorded for different Tokamak machines are shown and it is evident that JET experiment represents the forefront experiment on fusion. We can express the fusion device performance in terms of the Q factor, defined as the ratio between the power generated by the fusion reactions and that injected in the plasma, P H. Thus when we reach the ignition we have P H =0, that is Q. Actually it is not necessary for our purpose to reach the ideal condition in which no external power is required, the aim is to obtain high values for Q so to have an advantageous gain of energy. With JET we have reached Q=0.65 and ITER is intended to reach Q=10. For the future reactors the aim is to achieve Q~ α 6

15 Fig. 1.2: Performance of Tokamak machines in the world in terms of ntτ E on dependence of the ionic temperature. It is remarkable the improvement in the triple product higher than a factor 10 3 obtained in only 25 years Reactions of interest for the development of the controlled thermonuclear fusion The elements in the periodic table that undergoing fusion release a remarkable amount of energy and at the same time are quite easily to manage, are the lightest, i.e. the Hydrogen isotopes deuterium and tritium. The reaction d+d follows three branches, as shown in tab. 1.1, and the one of interest for thermonuclear fusion is d + d 3 He + n + Q (Q=3.27 MeV) (1.6) For the tritium we have the reaction d + t α + n + Q (Q=17.59 MeV) (1.7) The Q value represents the mass difference between fuel ions and products and it is therefore the kinetic energy available for these. The kinetic energy is distributed depending on the masses E n mimn = Q (1.8) m + m where E n and m n are the energy and mass of the neutron while m i indicates the mass of the ions produced in the reaction. Approximately we can say that for the first reaction E n =2.45 MeV and for the second one E n =14.1 MeV. i n 7

16 1.3 JET experiment The most promising device for realizing the nuclear fusion is the Tokamak (from the Russian words TOK (current) KAM (chamber) MAK (magnetic)). This instrument is based on magnetic confinement where the required fields are essentially constituted by two components: a toroidal one, produced by poloidal coils, and a poloidal component generated by the plasma current (fig. 1.3). The resulting total magnetic field has a helical shape which winds forming a torus. The plasma is heated up to hundreds of millions Kelvin, therefore it is crucial keeping it far from the vessel walls. The magnetic field lines are wound in loops forming closed lines and they are shaped in order not to touch the walls (fig. 1.3). However, ions can diffuse across the field so that it is necessary to direct the plasma into suitable target plates: this is realized through outer poloidal field coils beating the so called divertor. Fig. 1.3: Left: In a Tokamak plasma ions spiral along closed field lines forming a torus. Right: Example of plasma poloidal section in a tokamak (JET). The particular composition of the magnetic field lines gives the plasma a D shape. In the lower part the divertors, where exhaust plasma is collected and removed from the torus, are represented. 8

17 Fig. 1.4: System of coils which generate the magnetic field lines for confining the plasma at JET. The largest tokamak in the world is the Joint European Torus (JET) sited at Culham (UK). In fig. 1.4 the sketch of the magnetic components of the machine is shown. A transformer induces a toroidal current in the plasma and the plasma itself acts as secondary circuit of the transformer. The plasma pulse lasts a few tens of seconds. The plasma heats the plasma through the Joule effect. This mechanism has a limited intrinsic efficiency, because the higher is the temperature the lower is the resistance of the conductor and then the heating. The temperature reaches in this way at most millions of degree for a plasma current of millions of Amperes. To reach nuclear fusion, temperatures in the order of hundreds of millions of degree are required so that additional heating is necessary. Two techniques have been implemented at JET: the Neutral particle Beams Injection (NBI) and the Ion Cyclotron Resonant Heating (ICRH, also known as RF Heating). 9

18 Fig. 1.5: The electric current induced in the plasma heats this thanks to the Ohmic effect. Since this is not enough to reach temperatures for trigging nuclear fusion additional heating is required: actually the Neutral Beam Injection and the Radio Frequency play a dominant role Radio Frequency Heating Electromagnetic waves can be absorbed by the plasma and transfer their energy to the absorbing medium increasing in this ways the mean velocity of the chaotic motion of the ions, that is the temperature of the plasma itself: this is the mechanism of RF heating. The coupling between the electromagnetic wave and the ions can occur at characteristic frequencies. In our context the ions are moving around the torus following the field lines of an external magnetic field, B, with cyclotron frequency ν c =qb/m, where q and m are the charge and mass of the particle, and the above-mentioned coupling acts when the wave frequency equals ν c (therefore this heating mechanism is also known as Ion Cyclotron Resonant Heating, ICRH) qb ν = n (1.9) m where n is the harmonic number. By choosing the mass and the charge it is possible to select the ion target also controlling the deposition of the magnetic energy: the magnetic field decreases with distance from the center of the torus 10

19 (B 1/r) so that a specific region of the plasma can be heated. At JET four antennas placed in the inner wall provide waves with frequency in the range MHz, achieving a heating power up to 20 MW. The injected power, converted into kinetic energy of the deuterium (or tritium), creates a super-thermal ion population, which can undergo fusion with the thermal bulk of the plasma generating a super-thermal component in the neutron spectrum. The resonant particles are induced to move along circular orbits in poloidal planes of the torus, therefore generating neutrons by incidental fusion reactions having a preferential direction of emission. This component of the spectrum is therefore sensitive to the line of sight of the observer. Expedients must be put in practice utilizing RF heating. First of all the antenna must keep as close as possible to the plasma since the long wavelength of RF cannot propagate in the vacuum vessel. Another fundamental point is the frequency to emit. As described above this must be equal to the cyclotron frequency of the target ion, but this choice must be considered in the frame where the particle is at rest, so that higher harmonics are mostly applied. Fig. 1.6: NBI and RF system layout at JET. 11

20 1.3.2 Neutral Beam Injection heating The NBI heating is based on the injection of high energy atoms into the Ohmic plasma. The atoms injected, deuterium or tritium, become ionized gaining energy trough the electric field. Then they pass through a neutral hydrogen gas where, by charge-exchange processes, they get neutralized again so that they can penetrate the magnetic field confining the plasma. Here they undergo collisions in which they lose electrons allowing them to be captured by the magnetic field. The particles beam transfers its mono-directional kinetic energy through inelastic scattering of the ions and electrons so that the mean velocity of the plasma particles increases (and so the temperature). The beam needs enough energy to reach the centre of the plasma and at JET this energy is 80 or 140 kev for a total heating power of 23 MW. The ions that absorb the power injected and increase their kinetic energy can interact with the thermal bulk and emit neutrons in accordance with the reactions shown above and a super-thermal component of the neutron spectrum is then generated. There are two neutral injector boxes on JET, each can be equipped with up to 8 positive ion neutral injectors grouped into two banks with two and one passes through the plasma: the beam is injected in the plasma current direction and radially (fig. 1.6). Because of the nature of this heating mechanism there is a preferential direction in which neutron are emitted, so that the spectrum shape changes for detectors differently positioned. The studies conduced at JET are preparatory to the development of the next international fusion project ITER (International Thermonuclear Experimental Reactor), whose goal is to demonstrate the feasibility of nuclear fusion as source of energy, and with this aim the JET technical capabilities have been enhanced over the last few years. The main characteristics of JET and ITER are summarized in tab The vessel is provided with openings in wall in which instruments are placed in order to interact or study the plasma. Among these there are devices for the additional heating and neutron diagnostics. 12

21 1.4 ITER The International Thermonuclear Experimental Reactor (ITER) is the Tokamak machine projected to demonstrate the feasibility of using the thermal nuclear fusion as source of energy. The works for its built have already begun and it will be operating in In order to fulfill the purpose, the plasma must be similar to that required by a fusion power plant: this requires working with burning plasma for an indefinite time interval, then reaching the stationary state. For what concerns the magnetic and containment systems in the core of the plant they must be able to work all operations long since they will not be replaced; unlike the first wall, the divertor and the blanket modules where the remote handling is necessary, because of the presence of the radioactive tritium, and then the necessity of verify the efficacy of the methods of removal and substitution. Testing the heating systems (neutral injection and radio frequency) and the processes of the reaction products treatment (α particles and impurities) with the recycling of tritium, are other fundamental points. The construction itself represents a challenge with its huge dimensions: the plasma volume will be ten times that of JET and close to that of future commercial reactors. This demand on size is due to the fact that more volume implies more fusion reactions and better thermal insulation of the plasma, which means a large energy confinement time. The vessel will be more than twice large and sixteen times as heavy as any previously manufactured fusion vessel (comparison with JET characteristics is shown in tab. 1.2). This requires the development of sophisticated techniques, including for example advanced welding processes. 13

22 Parameters JET ITER Plasma major radius [m] Plasma minor radius (horizontal) [m] Plasma elongation ration Plasma volume [m 3 ] Plasma current [MA] Toroidal magnetic field [T] Ohmic heating [MW] 3 20 Neutral beam heating [MW] Radio frequency heating [MW] Duration of plasma discharge [s] Fusion power [MW] Q (Power generated/power injected) Tab. 1.2: Main parameters of JET and ITER The most expensive components will be the electromagnets that will be superconducting considering the strong magnetic fields required to confine the ITER plasma and the necessity of not wasting energy in form of heat through the conventional resistive electromagnets. There will be eighteen toroidal field coils, six poloidal field coils together with a central solenoid and some correction or shaping coils. The toroidal field coils are made by Nb 3 Sn, a material that can support very high magnetic fields, they are D shaped and they will be cooled to 4K, the liquid helium temperature, so to heavily reduce the resistance. The poloidal field coils will be placed in areas where the magnetic field is low enough to use another, more common, material containing niobium and titanium. To ensure that operations continue without any interruption, each coil has redundant turns so that any faults can be simply isolated and no replacing is needed. To 14

23 manage cryogenic systems is also important for removing impurities from the plasma, separating the waste gases into the different components for disposal or recycling fuel, cooling the sources for the radio frequency sources and controlling the gas pressure of neutral beam systems. In addiction to all these demands a reliable vacuum system is indispensable (for example to prevent heat in the atmosphere from boiling off the helium of the cryogenic system). The expected ITER lifetime is 35 years during which it will be capable of generating 500 MW of fusion power continuosly for at least 400s with a Q value ~ Heating in ITER The plasma heating systems provided for ITER are three: Neutral Beam Injection (NBI), Ion Cyclotron Resonance Heating (ICRH) and Electron Cyclotron Resonance Heating (ECRH). These methods assure the current drive and the high temperatures required. The NBI system is composed by three injectors (fig. 1.7) for a total power injected of about 50 MW and will be able to operate for long pulses, i.e. up to 3600 s for steady state operation. Differently from JET ions will be negative and it will be d - or H -. This choice is due the possibility of maximizing the efficiency of the charge exchange in the neutralizer: this is the chamber, filled with molecular deuterium d 2, where accelerated ions arrived and, without loosing their kinetic energy, they lose the negative charge according to d - + d 2 d 0 + d 2 + e -. The NB injectors are located on the north side, at the equatorial level of the tokamak building (fig. 1.10) and it is tilted to follow the structure of the machine. The initial setup will involve two neutral beams within the NB duct 8, the beam can be set at two extreme positions (on-axis and off-axis) by tilting the beam around a horizontal axis on its support flange. 15

24 Fig. 1.7: Layout of the ITER NB System in the horizontal plane. The frequency range of the ICRH will be approximately MHz: the frequency choice determines the coupling radiation-plasma (tab. 1.3). An extension of the frequency range to MHz could be possible facilitating a more flexibility but it would reduce the performance. The heating of tritium with a frequency ν=50 MHz acts on the toroidal magnetic axis. The main heating scheme is at the tritium second harmonic, 2Ω T, in a 50-50% DT mixture with ν=53 MHz and the toroidal magnetic field B T = 5.3 T with typical 50-50% power partition among the bulk ions and electrons. The presence of 3 He minority (< 3%) results in a significant increase of the fraction (up to 70%) deposited on bulk ions [5]. The tritium heating is off axis, precisely it results to be placed about 1/3 toward the external part of the torus. The deuterium minority heating scheme is less efficient because it is in strong competition with absorption by Be and α. The frequency window for on-axis current drive (FWCD) is at the peak of the electron absorption at ν=56 MHz. Ion minority current can be driven at the outboard for the control of the sawtooth period, at ν=45 MHz. There will be four equatorial ports available for providing a maximum RF power of ~80 MW; 16

25 two are expected to be used for the initial experiments. Resonance MHz Comments 2Ω T 50 On axis 2Ω T =Ω 3He 53 Second harmonic + minority heating - Off axis Ω D 40 Minority heating. Strong competition of Be and α FWCD 56 On axis current drive Ω 3He 45 Minority ion current drive at sawtooth inversion radius Tab. 1.3: Ion Cyclotron resonances The ECRH will use two types of RF launchers, operating at a frequency between 100 and 200 MHz: one type is located in an equatorial port and the other type is located in an upper port. The nominal injection power is 20 MW at 170 GHz and 2 MW at 120 GHz. The system will be used both for heating electrons population and for controlling the build up of certain instabilities, which could lower the temperature, heating the outer surface of the plasma. 1.5 Neutron diagnostics and neutron emission spectroscopy (NES) Plasma diagnostic is both active and passive. In the active method external probes are used to investigate the plasma while in the passive one, particle as well as radiation emission from the plasma is detected. Neutrons produced in dd and dt fusion reactions escape the magnetic field and can penetrate the vessel being detected at suitable locations around the tokamak. An example is the neutron camera which views the plasma in the poloidal plane through two multi-channel collimator arrays placed in a vertical and a horizontal port of the machine: this system defines a number of sight lines in the plasma to measure the line-integrated neutron emission. In this way the neutron emission profile and the neutron yield rate is determined. Capsules filled with materials as Cu, Mg and Si are used to measure the total neutron emission by measuring the radioactivity induced by neutrons. This system is also used to calibrate the other neutron diagnostics. Silicon diode detectors and fission chambers are also utilized to measure neutrons. The Neutron Emission Spectrometry (NES) is successfully carried out at JET using two spectrometers: MPR dedicated to neutrons produced by dd reactions and TOFOR, which can detect neutrons from both reactions dd and dt. 17

26 1.5.1 The MPR spectrometer The MPR is an upgraded version of a previous prototype installed at JET in 1996 and it is in use since Fig. 1.8: Sight line of the MPR in vertical and horizontal planes This device is located at 6 m from the torus and uses a horizontal diagnostic port, the solid angle of the Sight Line Cone (SLC) defined by a collimator is Ω n = 1.3 msr and its axis is inclined of 4.8 with respect to the equatorial plane (fig. 1.8). It is based on the (n, p) elastic scattering and subsequently proton energy measurement through momentum analysis (a scheme of the MPR is shown in fig. 1.9). This passive procedure of energy determination allows a high count rate capability (>>1MHz). The incoming neutrons pass through a collimator then the beam hits a polyethylene (CH 2 ) target where the neutron-proton conversion takes place. A proton collimator selects the protons scattered within angles of 7, which makes the energy transfer from the neutron almost complete, as the proton energy is E p E n cos 2 θ for θ 7 we have E p E n. The thickness of the conversion foil affects both the energy resolution E/E, defined as the response to monoenergetic neutrons, and the efficiency of the conversion, which is typically

27 10-4 cm 2. Protons are spatially separated depending on their energy by a magnetic field of about 1T generated by two magnetic multipoles, and they are directed toward a hodoscope, an array of 32 phoswich scintillator detectors. Fig. 1.9: Sketch of the MPR. The energy resolution value of the spectrometer can vary between % and it is connected to the loss of energy of the proton in the target, the ion-optical contribution (as the target image size on the focal plane) and the kinematics: the different resolutions are obtainable by varying some geometrical characteristics, as the length of neutron collimator and the aperture of the proton collimator. The scintillator crystals are coupled to two photomultiplier tubes through lightguides. The current is detectable as a voltage pulse which constitutes the data from the MPR measurement: by counting the number of pulses for each scintillator, a distribution along the hodoscope is formed and by knowing the response function of the spectrometer, it is possible to calculate the original neutron energy spectrum. In fig is shown a neutron spectrum as a function of the position along the hodoscope: the spectrum consists of a peak (centred around x 250 mm) due to the neutrons signal and a component connected to the scattered neutrons in the low energy range (x<200 mm). It is also possible recognize background events in the region x>350 mm likely due to cosmic rays. 19

28 TH INSCATTER Counts Counts Position, x (mm) Fig. 1.10: Example of spectrum obtained with the MPR spectrometer for neutrons produced by dt fusion reaction reactions (energy peak 14MeV). It is also shown the best fit to the data and in dashed the inscatter spectral component The TOFOR spectrometer The TOFOR, spectrometer based on the Time of Flight technique, is situated in the roof laboratory at about 20 m from the plasma (fig. 1.11), the neutrons passing through the floor are collimated so that a solid angle Ω n =0.35 msr is defined [6]. 20

29 Fig. 1.11: The TOFOR is placed in the roof lab and its line-of-sight is defined by the 1.90 m collimator through the torus hall ceiling. 21

30 Fig. 1.12: The energy of the incoming neutrons is given as a function of the flight time between the S1 and the S2 detectors. A fraction of these neutrons undergoes n+p elastic scattering into the S1 scintillator in turn generating recoil protons which constitute the first signal detected by the spectrometer. The second signal is produced by the scattered neutron interacting in the S2 scintillators placed on the surface of the TOF sphere whose radius is R=70.5 cm. The length of the S2 elements covers an angular interval of 30±7.1 relative the S1 detector (fig. 1.12). The scintillator S1 is of circular shape and it consists of five elements, each element being connected to three light guides. The crown of S2 scintillators is made by 32 trapezoidal shaped elements, each one being coupled to the base a light guide that lead the signal to the PM tube. As the technique is based on neutron scattering and time coincidences measurements, scintillators with high Hydrogen content and a good time performance are needed. Plastic scintillators have been chosen to fulfill these requests. Neutrons incident on an element of S2 produce a light signal which travels along the scintillator before reaching the PM tube: a propagation time difference is present between neutrons incidents near the PM tube and on the opposite part of the scintillator element, and the maximum time difference is of 2.4 ns. In order to compensate for this effect each S2 element is rotated around its 22

31 centre coordinates so that the flight path results shorter and longer for large and small neutron scattering angles respectively. With an inclination of 5 we can reduce the difference in the propagation time to 1 ns. Neutron energies between 1 MeV and 5 MeV correspond to flight times in the range ns that is a time interval between the signal in S1 and S2 of about 60 ns. In the TOFOR spectrum are reported events preceding till 200 ns the signal detected in S2. The coincidence windows are applied in the data reduction phase and can be adjusted to fulfil purposes at hand I [a.u. ] I [a.u #69388 # t tof [ ns] ttof [ns] Fig. 1.13: Exemplum of two TOFOR spectra observed for neutrons generated by dd reactions (the two set of data refer to different conditions of heating of the plasma). The higher energies neutrons are on the left part of the plot, they correspond to the smallest time of flight values Neutron flux diagnostic at JET Plasma profiles don t vary significantly along the toroidal direction because here plasma particles move freely and then any local perturbation is immediately spread along the magnetic field lines. This constitutes a good advantage for the observation of emitted radiation: as a matter of fact it is enough to observe along a poloidal plane to know the global behaviour of the plasma torus. The Neutron Camera was built on this principle (fig. 1.19), allowing knowing the total neutron flux and the neutron profile. Two cameras with multichannel collimators look the plasma along 10 horizontal and 9 vertical lines of sight. For each line of sight neutrons are measured with NE213 liquid scintillators, for both 2.45 and 14 MeV 23

32 neutrons, and with plastic scintillators (by Bicron-418) for the detection of 14 MeV neutrons. To exclude neutrons scattered off the structure, a threshold of 2 MeV has been set. The Activation Monitor is based on the neutron activation: foil samples (such as Cu, steel, Si, Mg, Al) are placed close to the plasma. Upon neutron irradiation these will decay emitting γ radiation whose rate is related to the number of neutrons that hit the foils. The foil is inserted with a pneumatic system into one of eight positions close to the plasma edge (fig. 1.14). The silicon diodes are dedicated to the detection of neutrons of 14 MeV. The main reactions involved are: 28 Si+n 25 Mg+α and 28 Si+n 28 Al+p. Three sets of Fission Chambers, two 235 U cambers and one with 238 U, estimate the local neutron flux. The neutrons induce fission in the chambers materials and then the energetic fission products are counted in an ion-chamber: the current and the pulse frequency produced are proportional to the number of fission events and these are proportional to the number of incoming particles. Fig. 1.14: Localisation of the radiation ends of JET activation foil diagnostic in the poloidal cross-section. Eight radiation ends are located in four octants (up). Foils of the Activation Monitor are placed close to the plasma in 8 positions (three positions are duplicated at two different toroidal locations) (down). 24

33 1.5.4 Neutron diagnostic at ITER In planning the diagnostic instrument for the ITER experiment it is necessary to consider the intense neutron flux that will run over all the plasma surroundings. The expected total flux is ns -1 cm -2 with a maximum flux at the first wall of ns -1 cm -2 [7]. For comparison at JET during the campaign in which the highest neutron yield was obtained (1997, Y n = n/shot with the maximum neutron rate was ns -1 both for dd and dt neutrons), the neutron flux at the first wall was ns -1 cm -2 for dt neutrons and the total flux (dd, dt and scattered n) was ns -1 cm -2, whereas the neutron flux of only 14 MeV neutrons was about ns -1 cm -2. Considering such hard conditions in ITER a programme is being carried out in order to produce diagnostic techniques and technologies to be compatible with the described environment. System already experimented with JET are planned: neutron cameras with a radial and four vertical arrays of line of sight, fission chambers containing 235 U or other isotopes and two activation systems. Finale choices regarding neutron spectrometers have yet to be made due to interface restrictions. It is nevertheless clear that at least one high performance spectrometer will be installed on ITER. 25

34 2 Neutron emission Different processes producing neutrons take place in fusion plasma and the observed neutron spectrum is a fingerprint of these. Each fusion reaction generates a neutron distribution with a characteristic shape that contributes to the total spectrum with a different weight, depending on the energy range. In these distributions, we can identify two main regions: a predominant peak, which represents the THERMAL emission from the plasma, and an HIGH ENERGY component whose shape depends on the specific neutron generating process. In the next paragraphs those events that may contribute to the high-energy part of the neutron spectrum will be described. The low-energy side of the spectrum is not significant for any investigation of the plasma properties because of the inscattering and back-scattering components that can distort the shape (see the example in figure 1.10). 2.1 Fusion neutron kinematics For the interpretation of the observed neutron spectra we make use of calculation models starting from the kinematics of a single fusion reaction. In this paragraph the reaction d+t n+α is considered, but analogous arguments are valid for d+d n+ 3 He. From energy and momentum conservation the neutron energy can be easily derived in the center of mass reference system (CM) and then transformed in the laboratory system frame using non-relativistic kinematics leading to the expression: E n mnmα ( Q + K) + mnvcm + VCM cosθ ( Q + ) α 2 mn + mα = mα m + m K n (2.1) Here m α and m n are the masses of the reaction products, Q is the mass difference of the reactants and products, θ is the angle between V CM and the neutron emission direction. V CM and K are the neutron velocity and kinetic energy in the center of V mass reference system, i.e. CM md v = m d d + m v + m t t t and K=½µ v rel 2, where v d, v t are the reactant velocities in the laboratory system, v rel the relative velocity between 26

35 the reacting ions, µ the reduced mass. In figure 2.1, the sketchs of this reaction in the CM and lab systems are shown. v α v t v CM v α v CM θ v n v t v d u n v d CM system lab system Fig. 2.1: Kinematics of the reaction d(t,n)α in the centre of mass and lab system. If more reactions take place, we observe a broadening around a central value E 0 in the neutron spectrum, due to the presence of the term V CM cosθ that is the projection of the centre of mass velocity along the direction of the neutron velocity in the CM system. In a thermal plasma the distribution of V CM is isotropic and the Doppler broadening is proportional to the square root of the ion temperature T i ( 2.2.1). The central value for E n in dt reactions is the theoretical 14.1 MeV, calculated considering the reactants at rest. Actually, ions have a certain amount of kinetic energy therefore this value results to be higher. The plot in Figure 2 shows the energy of a neutron emitted by a head-on dt reaction for a fixed deuterium energy and in dependence of the tritium energy: we can see that for tritium energy values close to zero the neutron energy is close to 14.1 MeV. To calculate the neutron spectrum R(Ω, E n ) emitted by a small volume of uniform plasma the integral of eq. (2.1) must be carried out over the velocity distributions f d (v d ) and f t (v t ) of the reactants. It is furthermore necessary to calculate the line integral over the values of the plasma parameters as functions of the position in order to take into account the specific line of sight, whose solid angle is Ω, trough which the spectrometer observes the plasma. From the analytically point of view the following integrals must be solved 2 d R n d ntvn µ µ = f + d v n u n v rel ft v n u n + v dωden 2πm n md mt rel v σ ω ( vrel ) 2 3 δ ( u u ) 2 d v d w rel 3 n n0 rel (2.2) 27

36 E t [MeV] Fig. 2.2: Energy of neutron emitted in dt head-on reaction, i.e. cosθ=1, as function of tritium energy. The deuterium energy is E d =0.015 MeV. where n d and n t are the reactant densities, σ(v rel ) is the reaction cross section ( 1.1.1), v n and u n are the emitted neutron velocities in the lab and CM systems respectively, δ is the Kronecker delta function, u n0 = (2 E 0 /m n ) and E 0 =(Q+K)m α /(m n +m α ). This procedure is developed in [8] where some examples are also shown in the case of simple expressions for the reactant distributions. A remarkable result concerns a plasma at thermal equilibrium in which the reactant velocity distributions can be expressed by isotropic Maxwellians: the neutron energy spectrum results to be nearly Gaussian with a Full Width at Half Maximum proportional to the square root of the reactant temperature FWHM T i. A different approach is to employ numerical techniques for integrating eq. (2.1). This is the strategy we adopted: by using simulated neutron spectra employing the ControlRoom code which makes use of the Monte Carlo method ( 2.2). The mean neutron energy undergoes a shift E r due to the plasma rotation. It is possible to evaluate this contribute to the velocity from (1) by adding the term V r cosα, where α is the angle between the rotation velocity V r and the sight of line. If the rotation occurs in the sight of line direction we obtain 1 2mnm 2 α 1 2 Q + mnvr n + mα 2 EV = Vr, where E r is in kev, V r in km/s and m 28

37 the kinetics energy has been neglected since Q>>K. 2.2 Emission processes For thermonuclear plasmas at equilibrium, the main neutron spectrum component is due to the thermal emission in which bulk ions react directly to produce neutrons. When additional heating is applied, such as ICRH and NBI ( 1.2.1), the same kind of reactions give rise to a more energetic component in the neutron spectrum because of the presence of high energy ions: these contributions are relevant for JET experiment while for ITER the neutron spectrum will still be essentially thermal. Components in the spectrum are produced by AKN and HKN (α and 3 He Knock-on Neutron emission) processes that take place in DT and DD plasma, respectively. Nevertheless, the study of the AKN contribution is of great relevance being the signature of the confined α particles (whose importance was discussed in 1.1.2). In deuterium plasmas we must also consider the TBN (Triton Burn-up Neutron emission) whose study contributes to gain information on the fast particle confinement and from these measurements it is therefore possible to extrapolate insight into the α particles behaviour in DT plasma Thermal emission Ions that undergo fusion emit particles at specific energies. In DD plasma the fusion reaction of interest is d+d n+ 3 He (2.3) Considering reactants at rest, the available energy for the products is Q 3.3 MeV which is distributed between the products in accordance with the kinematics of the reaction. For the neutron we obtain E n0 m3he = Q (2.4) m + m n 3He that is E n0 =2.45 MeV. For DT plasma neutrons are generated by the reaction d+t n+α (2.5) For this process Q 17.6 MeV and 14.0 MeV of this amount is carried away by the neutron. In a real plasma the reactants are not at rest, but they have a kinetic energy. For an Ohmic plasma the thermal motion of the interacting ions causes the 29

38 reaction products spectrum to spread around the characteristic energy. For stationary plasma with Maxwellian distribution of the ion velocities, the products energy distribution is nearly Gaussian [8] ( ) 2 1 E n En0 s(e n ) = exp 2 (2.6) 2πσ 2σ n n where E n0 is the characteristic energy of neutrons for a given reaction and σ n the standard deviation. As a matter of fact, the hotter the plasma, the broader the neutron distribution, so that through the study of the thermal neutron spectrum the temperature of the reactants can be inferred. In particular this information lies in the FWHM in accordance with FWHM = k (2.7) T i where the constant depends on the reactants masses and it is and 83.8 for dt and dd reactions respectively [9]. Things are more complex for real plasma confined in a Tokamak since there is not uniformity both in density and temperature. Therefore the resultant spectrum is the composition of different Gaussian spectra and what it is observed depends on the specific region of the plasma crossed by the line of sight of the detector (this is discussed in detail in chapter 3) The AKN and HKN emissions We know from eq. (2.1) that in dt fusion reactions α nuclei are generated with energies 3MeV, that is with energies much higher than the bulk ions. These high energy ions slow down in the plasma thermalizing over times in the order of 1 s. This energy loss takes place through multiple low angle scatterings off plasma ions and electrons. It may happen that some α scatter deuterium or tritium particles, d(t), in a head-on collision: since in these unlikely processes a substantial amount of the α energy is transferred, it comes out that the energy bulk is remarkably enhanced. As described for the α particles, these high energy ions, d (t ), undergo thermalization, but during this process fusion reactions can take place giving rise to a super-thermal neutron population, n. This is the Alpha Knock-on Neutron emission (AKN) that even if it constitutes a component of the neutron spectrum (its relative intensity with respect to the thermal component is 10-5 ), it dominates the high energy region (E n 15.5 MeV). It is a three steps 30

39 process summarized by the following reactions: (1) d+t n+α α slowing down (2) α+d(t) α +d (t ) d'(t') slowing down (3) d +t n +α or d+t n +α The analogous process occurs in DD plasma involving 3 He nuclei produced by fusion reactions or introduced as impurities. The energy of these ions when bred by fusion reactions is lower than 1 MeV, therefore in order to have a significant effect in the neutron spectrum it is necessary to heat the 3 He by ICRH (chapter 4). The AKN or HKN contribution to the neutron spectrum is observable depending on the characteristics of the heating method that can enhance one component or another. Aiming to identify the conditions in which the different contributions can be detected in ITER, different heating scenarios have been studied for a tangential and a radial sight line: the detailed discussion and the results are presented in paper.. included in the second part of this dissertation. As an example, in figure 2.2 a simulation referring to a plasma scenario with ICRH resonating at 53 MHz in an ITER plasma Total RF B AKN E[MeV] Fig. 2.2: Simulated neutron spectrum for tangential line of sight. The total neutron spectrum is shown together with the contribution from bulk (dashed line), radio frequency (dotted line) and AKN (dot and dashed line) components. 31

40 2.2.3 TBN The fusion between two deuterium ions producing one neutron is not the only one fusion reaction that involves deuterium. We observe in table 1.1 that the other important branch is d+d t +p (2.8) in which a tritium ion is produced with E t 1 MeV. These fast tritons remain confined in the magnetic field of the torus where they are thermalized by means of low angle scatterings off ions and electrons. During this process they can react with the deuterium generating a supra-thermal 14 MeV component in the total neutron emission d+t n +α (2.9) Being this neutron component in a higher energy range with respect to the thermal bulk emission it can be quite easily revealed and through its study information on fast ion confinement is provided. 2.3 Monte Carlo simulations Simulations of the neutron plasma emission are performed through the ControlRoom code [10]. The original system consisted in a C++ library and some applications whose programming language is Python. The original aim of the code was calculate the slowing-down ion distribution in thermal plasma and the resulting neutron emission, but it is in continuous development and nowadays it can address more tasks [11]. The neutron spectrum calculation is computed by the library function CalculateSpectrum. As we have seen in the first paragraph the expression for the neutron spectrum is given by Lehner and Pohl in [8] ( 2.1). The numerical way to handle such double integral is by means of a Monte Carlo method, an approach that takes advantage of its intrinsic simplicity in opposition to the analytical one which can be applied to relatively simple cases only. We can therefore use any kind of reactant distribution and consider anisotropic cross sections if it is the case. Particular relevance for the calculation of the minor components of the spectrum is the possibility of using numerical data as input for calculations. 32

41 A certain number of single reactions are simulated, for each of those the velocities v a and v b of the nuclei reactants are chosen from the known velocity distributions using pseudo-random numbers. In particular it is assumed that the velocity distribution function can be written as a function of the spherical coordinates, i.e. f(v)=v(v)θ(θ)φ(φ). Thanks to this factorization to associate two velocities v a and v b is equivalent to apply the random number method to the three monodimensional velocity functions for each of the reactants a and b, that is the code executes six pseudo-random number extractions. It is also possible to add a toroidal velocity component which takes into account the collective motion of the plasma ( 2.1). In accordance to the equation (1.1) we know the energy of the neutron emitted along the sight of line direction, with the probability given by the product σ(v rel,θ)v rel (see 2.1). The neutron spectrum results from a weighted statistics of a great number of such events. Into the SlowingDownDistribution class there is the calculation of the distribution function of energy particles that undergo a slowing down process caused by multiple scattering with the electrons and thermal ions of the bulk. The steadystate distribution for an isotropic source Q(v,t) of fast ions is given by τ s 2 f ( v) = v Q( v) dv 3 3 v + v C v (2.10) where τ S is the Spintzer time [12] and v C is the critical velocity for which the slowing-down particle give its energy to both bulk ions and electrons. For the purpose of this work we are interested in α or 3 He particles: these fusion products can transfer a significant amount of their energy to the thermal ions through large angle scattering and these can produce an high energy component in the neutron spectrum as described in We calculate at first with ControlRoom the products (n, α or 3 He) distribution functions of thermal bulk trough CalculateSpectrum, the function SlowingDownDistribution defines the profile of the α or 3 He particles afterwards. The production of the dd (or dt) high energy tail from scattering processes is performed by CalculateSpectrum and then processed by the function SlowingDownDistribution: the resulting high energy reactants are used as input by CalculateSpectrum to calculate the high energy neutron component. 33

42 The torus plasma has been defined trough a certain number of cells and just a part of these are involved in the described computing procedure, considering the fact that the real diagnostic instruments receive radiation just from a region of the plasma which is defined by the collimator. For example in our simulations for JET, the cells are chosen according to the line of sight of the MPR and TOFOR spectrometers ( 1.4.1, 1.4.2). 34

43 3 Sight line effects Spectrometers observing the plasma through different lines of sight (SL) detect different spectra depending on the properties of the reactants in the plasma volume intercepted by the SL. Is it possible to gain diagnostic information by the neutron emission spectroscopy (NES) when observing simultaneously the plasma through two different SL? What are the SL effects on the revealed temperatures? Is there a SL that can be considered more advantageous? What is the most desirable SL configuration for the neutron spectrometers of the next fusion experiment, ITER? These are the questions that will be addressed in the following paragraphs and in three papers collected in the dissertation. 3.1 Thermal neutron spectrum: local and observed As we saw in 2.2.1, for Ohmic plasmas the neutron spectrum is Gaussian and it is possible to infer the temperature of the reagent ions in accordance with FWHM = const (3.1) T i where the constant depends on the reactants masses. For a real plasma confined in a tokamak, which is not uniform both in density and temperature, the resultant spectrum is a superposition of Gaussian distributions, each with a temperature related to the region of emission. Thus the observed temperature, T eff, is a weighted average given by T(r) y (r) dr V Teff = (3.2) y (r) dr where y n (r) = n 1 (r) n 2 (r) <σ v> T(r) is the emissivity, n 1 (r) n 2 (r) the local ion V n n density of the species 1 and 2 and <σ v> T(r) the reactivity. The effective temperature is therefore smaller than the maximum value of the ion temperature, T 0, depending on the regions crossed by the SL. In two works it is studied the influence of the SL on the observed temperature and the possibility of gain diagnostic information on plasma parameters as a result of two distinct SL instead of one. With this purpose, simulations of the neutron 35

44 spectrum have been carried out as observed by the two JET spectrometers, MPR and TOFOR ( and 1.4.2). Different scenarios of thermal plasmas confined in a tokamak have been considered and T eff have been calculated by performing a Gaussian fit. We have considered deuterium-tritium (dt) reactions, even though the TOFOR reveals neutron produced only by dd reactions. Furthermore here we focus on Ohmic plasma, even if it is not the dominant component for JET plasmas. Indeed, studying the condition of steady thermonuclear burn of DT plasma is fundamental in view of the next fusion experiment ITER ( 1.3). In order to have a general scenario on the ion profile dependence of T eff and to examine what obtained by the simulations, an analytical calculation of T eff from eq. (3.2) has been done for parametrized SLs, assuming a simplified geometry: circular plasmas, in contrast to the elongated one of JET, and pencil-like SLs with no lateral extension. 3.2 Thermal neutron spectrum: simulations Neutron spectra have been produced by Monte Carlo simulations and apparent temperatures deduced by fitting a Gaussian lineshape. Simulations have been performed by using ControlRoom code ( 2.2): this software calculates the neutron spectrum produced by a plasma with given initial ions distributions, as observed by a SL that crosses one defined torus geometry. First we considered an Ohmic Plasma confined in a torus with JET geometry (elongation 1.3) for different plasma conditions. In order to study the viewing line effects on NES we referred to the Sight Line Cones (SLC) of the MPR and TOFOR. MPR is located at 6 m from the torus and uses a horizontal diagnostic port, the SLC solid angle is Ω n = 1.3 msr and its axis is inclined of 4.8 with respect to the equatorial plane; TOFOR is situated in the roof laboratory at about 20 m above the plasma with Ω n = 0.30 msr. The two instruments view the torus through a quasi-tangential SL in the horizontal plane (fig. 3.1) and a vertical SL through the plasma centre respectively (fig. 1.11). The spectrometer collimators intercept a volume in the plasma characterized by a certain temperature and ionic density distribution. Plasma parameters, such as density and temperature, can be considered constant on the magnetic surfaces while they show a dependence on the distance from the plasma centre. This feature can be described by the analytical expressions 36

45 2 T ( ρ ) = T (1 ρ ) 0 α T (3.3) 2 αn 2 4 n ( ρ) n (1 ρ ) [1 + β ( ρ + )] (3.4) = 0 n ρ where ρ=r/a, a=1m is the JET plasma horizontal minor radius, T 0 and n 0 are scale parameters, α T, α n and β n are profile parameters. Fig. 1.1: Projection of the MPR sight line cone (SLC) on the poloidal section of the torus plasma in JET. The full lines represent the part of the SLC (the axis and the extreme chords) nearest to the MPR, while with dashed lines the part from the minimum radius to the exit from the plasma 37

46 β n =0 α n =0.5 β n =0 α n =10 β n =10 α n = ,5 0 0,5 1 r/a Fig. 3.2: Examples of neutron ion density profiles used as input for the simulations As far as the temperature profile is concerned, the values varied in the code are the central temperature T 0 and the shape parameter α T. Central temperatures range from 5 to 25 kev in steps of 5 kev and α T =0.5 and 3.5, corresponding to two confined modes, i.e. the H mode and the ITB mode respectively. Other input parameters are α n and β n. For the latter were chosen two representative values: β n =0, for the peaked profile, corresponding to a maximum density in the centre regions of the plasma, β n =10 to describe a hollow profile (fig. 2). The neutron emission depends on the ion temperature and density profiles, so that for a given set of T 0, α T and β n, it is possible to choose α n in order to obtain a desired width for neutron profile. In particular the value for the fractional width w, defined as the neutron distribution width from the centre of the distribution at half maximum dived by 2a was fixed (table 3.1). Values cover a wide range and obviously it is possible to reach larger width for hollow profiles. 38

47 α n β n =0 α T =3.5 β n =10 α T =0.5 T 0 [kev] w=0.17 w=0.19 w=0.20 w=0.22 w=0.3 w=0.45 w=0.7 w= Tab. 3.1: α n values used in the simulations for peaked (left) and hollow (right) neutron emission profiles. In italics the values used for the examples in fig In bold the scenario used for the simulations shown in fig In fig. 3.3 two examples of spectrum obtained for DT plasma observed through the TOFOR and the MPR SL are shown, together with the Gaussian fit. Through the fit we obtain the FWHM and in accordance with the eq. 3.1 (using for the constant [7]) the temperatures T eff. In fig. 4 are presented the results of the simulations as the relative difference of the temperature that the two instruments should measure, with respect to the central temperature T 0 for both neutron profiles. We can summarize the different scenario noting that each T eff is connected to a couple of plasma parameters, namely w and T 0. The plots in fig. 5 and 6 show the difference in the T eff revealed by the two instruments, in particular the ratio TTOFOR T T TOFOR MPR peaked and hollow profiles. in dependence of T TOFOR, respectively for the case of the 39

48 10 9 MPR 10 8 TOFOR E[MeV] E[MeV] Fig. 3.3: Examples of the simulated thermal neutron spectra from a DT plasma obtained with the Controlroom code considering the SLC of MPR and TOFOR. The plasma parameters used are those in bold in table 3.1. The dashed lines are Guassian fits. 0,3 hollow neutron distribution peaked neutron distribution 0,25 0,2 0,15 0,1 0, T 0 [kev] w=0.85 w=0.70 w=0.45 w= T 0 [kev] w=0.22 w=0.20 w=0.19 w= Fig. 3.4: Results for T eff obtained from Monte Carlo simulated spectra for the MPR and TOFOR spectrometer viewing DT plasmas with temperature and density profiles as explained in the text. Shown are the fractional differences (T 0 - T eff ) /T 0 as function of T 0 for T 0 =5, 10, 15, 20, and 25 kev. Dots refer to MPR and crosses to TOFOR. 40

49 w =0.17 y w =0.19 y w =0.2 y w =0.22 y T TOF [kev] Fig. 3.5: Comparison of T eff calculated for TOFOR and MPR for a DT plasma in the case of a peaked neutron emission (β n =0) and α T =3.5. The dashed lines refer to iso-temperature T 0, the different symbols to iso-width of the neutron emission profile. 0,08 0,07 0,06 0,05 w=0.3 w=0.45 w=0.7 w=0.85 0,04 0,03 0,02 0, T TOF [kev] Fig. 3.6: Comparison of T eff calculated for TOFOR and MPR. Simulation refers to dt reactions and to a hollow neutron emission (β n =10) and α T =0.5. The dashed lines refer to iso-temperature T 0, the different symbols to iso-width of the neutron emission profile. 41

50 3.3 Simulated thermal neutron spectrum: results As mentioned above, the temperature T eff revealed by an instrument whose SLC crosses the plasma in regions where there is a temperature gradient results to be lower than the maximum T 0 and the specific percentage depends on the relative integration volume. Through simulations we find for the hollow neutron distribution scenario that for the MPR spectrometer the values varies from 5% to 29%, that are very close to the range 3% - 25% of TOFOR (fig. 3.4). When the neutron emission is peaked we find for MPR temperatures in the range 17% - 25% of the maximum and from 9% to 14% for TOFOR (fig. 3.4). As we can expect from a SL that crosses mainly the central region, the obtained temperature is quite close to the central value, while for an integration volume including a larger portion of the outer plasma T eff is farther from T 0 : this is reflected by the percentages reported above and this behaviour is more pronounced in case of peaked neutron emission. In fig. 3.5 and 3.6 it is possible to recognize a clear trend toward larger difference between what is observed by the two LS with the increasing of the width of the neutron distribution in both hollow and peaked neutron profiles. It can also be noticed that the scenarios of plasmas with the same neutron emission profile lie on nearly constant lines: this reveals that the difference in the measured temperature from different SL is not affected by the maximum temperature of the plasma but only by the profile of the emitted neutrons. A remarkable property shown by these plots is that the temperature observed by TOFOR, which has a radial SL, is always higher compared to what observed through the SL of the MPR, which uses a horizontal SL. This happens for every kind of plasma profile. This will be discussed in the next paragraph. We can notice that the combined use of two SL provides profile information, namely the maximum temperature of the plasma and the width of the neutron profile. This is possible since the temperatures observed by two SL identify a point in the plane of a plot like in fig. 3.5 and 3.6. Considering uncertainties, they identify a rectangle of possible pair values w-t 0, obtained under opportune hypothesis about plasma profile shapes. 42

51 3.4 Analytical calculation Considerations about the SL placement, using an analytical model, can explain the achieved results. The analytical T eff calculation was carried out in accordance to eq. 3.2, assuming circular plasma with a parabolic neutron distribution y n (ρ)=y n0 (1-ρ) αy, where ρ=r/a is the radial parameter. The value α y was chosen in such a way to give a width w yn =0.3 and for the temperature profile was used α T =3.5 as representative average for JET plasmas. In order to have a systematic study of the SL dependence of T eff different SLs were specified on the basis of geometrical parameters with the simplifying assumption of pencil-like SLs with no lateral extension. The radial SL lying on a poloidal cross section (fig. 3.7 (a)) was specified by a normalized radial impact parameter p R =P R /a, where P R is the SL distance from the cross section center A: the vertical TOFOR SL is a radial SL with p R 0. The horizontal SL lying on the horizontal plasma midplane was specified by a normalized horizontal impact parameter p H =(P H -R 0 )/a, where P H is the SL distance from the torus centre O (fig. 3.7 (b)) so that a SL tangential to the plasma axis circle of radius R 0 would have p H =0. With this representation an inboard SL with 1<p<0 makes a double pass through the hot plasma core near the plasma axis, whereas outboard SL do not cross the plasma axis circle. Tilted SL is obtained by tilting a horizontal SL by an angle β in the vertical plane containing the horizontal SL (fig. 3.7 (c)). Two pivot points for the tilt were considered: the point A of intersection of the horizontal SL with the plasma axis (for inboard SL only), and the point B of minimum distance of the horizontal SL from the torus centre. Both points are shown in fig The MPR SL is tilted with p H 0.85, β 4.8 and pivot point A. 43

52 R (a) P R A a (b) O R 0 (c) P H H A a B H A B β Fig. 3.7: Schematics of SLs used for the analytical model: (a) Radial SL lying on a poloidal cross section; PR is the SL distance from the cross section center A. (b) Horizontal SL lying on the horizontal plasma midplane; PH is the SL distance from the torus center O. A is the first intersection of the SL with the plasma axis circle. B is the SL point closest to the torus centre O. (c) Tilted SL obtained by tilting a horizontal SL by an angle β in the vertical plane containing the horizontal SL. Points A and B in (b) are used as pivot points. 44

53 3.5 Results of the analytical calculations T eff T In fig. 3.8 the relative T eff deviation ( δ = T 0 0 ) is plotted for both radial and horizontal SL with β=0 versus p R and p H respectively. The smaller the δ value the closer T eff to T 0. In the case of the radial SL the δ(p) curve is symmetric about p=0. Radial SLs that do not intercept the axis have a lower T eff and at the plasma edge (p=±1) T eff goes to zero and the discrepancy δ is 100%. The horizontal SL has the same trend for the δ(p) in the region p 0.27 and a minimum value ~7.5% that occurs for p Further inboard it rises up to a maximum of 19% at p= 0.5; it then falls slowly toward an asymptotic value. For p 0.27 the two curves show a discrepancy that becomes very pronounced for the innermost regions, in particular the radial SL perceives a temperature lower than the Horizontal SL. We can interpret this as a double pass of the horizontal SL through the hottest central part of the torus plasma against the single pass of the radial SL, so that in the former case a higher proportion of neutrons generated by hot ions arrive to the detector and higher temperatures are revealed δ Radial 0.2 Horizontal p Fig. 3.8: The relative T eff deviation δ calculated for radial SL, plotted vs p R, horizontal SL, plotted vs p H with β=0. We consider now SL tilted relative to the horizontal plane with β=5 and 10. The results on the calculated effect are shown in fig. 3.9 on T eff (p H ) for the two choices 45

54 of pivot points. Numerical results only apply to a specific choice of parameters but we can make general observations. Considering the region p~0, the higher the β angle the higher the δ values. This reflects the fact that the SL intersects more and more peripheral parts of the plasma with increasing β, thus lowering T eff of these centrally peaked profiles. Looking at lowest p values, δ(p) shows a minimum before rising as p decreases towards p=-1. This effect is reduced when the pivot point is placed on the plasmas axis, for which δ(p), after a maximum, slightly decreases to a constant level: the tilt angle effect on T eff comes mostly from the exit side but there is always one crossing of the SL through the hot core. In the case of pivot point B, the trend is more similar to a radial SL. Actually, a tilted SL with β=90 and pivot B is a vertical SL, i.e., same as radial. The MPR SL crosses the torus on the magnetic axis plasma (fig. 3.1) with a tilted angle β=4.8 and p= 0.85, so we can refer to the result obtained for the SL with pivot point A and β=5 and compare it with the TOFOR value on the R curve: both SL are marked in fig For the MPR SL δ(p)~25%, that is T eff 15 kev for T 0 =20 kev, and δ(p)~17.5% for TOFOR that would therefore reveal as temperature T eff 16.5 kev. Thus the analytical calculations give the same results obtained with Monte Carlo simulations. 46

55 1 B-10 R B-5 A-5 A-10 H p Fig. 9: The relative T eff deviation δ calculated for tilted SL, plotted vs p H with β=0 and 10 and pivot points A or B (curve A: 5, curve A: 10, curve B: 5, and curve B: 10 ). Also the Radial SL (black curve R) and the Horizontal SL not tilted (blue curve H) are shown. Full circles mark the SLs used by the neutron spectrometers at JET: MPR is at p H = 0.85 on A 5 curve and TOFOR is at p R =0 on the R curve. The horizontal line marks the asymptotic value of δ R min =16.5% (see text). 47

56 3.6 SL effects on absolute neutron yield The measure of the absolute neutron yield Y n is based on the following methods at JET (see 1.4.3): (a) Fission chambers reveal the uncollimated neutron flux F n. Through a calibration it is possible to know the relation between F n and Y n, so that fission chambers are used as yield rate monitor over the range 1 MeV-14 MeV. (b) Neutron cameras are arrays of detectors which look at the plasma through collimators which define observation chords crossing the plasma in the poloidal plane. The total neutron yield is given by summing all contributes after the required calibration of the cameras. A third method uses a spectrometer, once identified the part of the detected flux that is due to the neutrons directly emitted from the plasma with respect to the scattered one. Also in this case the key point is to determine the proportional factor, say C, between the observed flux F n and Y n. As described in the previous paragraphs, the spectrometer observes the torus along a cone that includes a defined volume of the torus plasma. Thus the measurements depend on the neutron emission profile and the C value changes with y n (r). This means that one must have information on the neutron emissivity distribution over the plasma volume which is obtained for example from neutron cameras (fig. 3.10). But this situation, besides being a constraint, is also not always possible to realize. To go in depth into this problem an analytical and systematic study on the SLs was developed in order to assess the sensitivity of these to the neutron emission profile ([P2] G. Gorini, J. Källne, F. Ognissanto, M. Tardocchi, Relationship between neutron yield rate of tokamak plasmas and spectrometer measured flux for different sight lines, Report MIB-NGS ). It came out that some SL are less sensitive than others to y n (r) (fig. 8 in [P2]) and this peculiarity makes them more privileged for our purposes, since for them there is no need of knowing the neutron profile information to obtain the total neutron yield. In particular, it was found that MPR SL is close to optimum from this point of view. 48

57 1E+19 1E+18 Yn MPR 1E+17 1E+16 1E+16 1E+17 1E+18 1E+19 Yn monitor Fig. 3.10: Example of deduced information on the absolute neutron yield rate, Y n (t), derived from the MPR measured neutron flux for DT plasmas compared with the results of the neutron flux monitors calibrated to provide Y n (t) [IAEA paper]. 3.7 SL considerations on ITER The described study on the SL was carried out with reference to the JET plasma geometry and spectrometers. Actually at JET the main component of the neutron spectrum is not of thermal origin, but emissions of other nature dominate ( 2.2). As mentioned before, the benefit of such studies relies on a wider perspective, since the results will be of direct relevance for future burning plasma experiments on ITER ( 1.4) where thermal reactions will dominate. In addition to this, the importance of the choice of the SL emerges also in consideration of the minority neutron spectrum components: these are essentially due to the AKN process ( 2.2.2) and as a consequence of the RF and NBI ion heating ( 1.2.1). In a context where the neutron spectrum is dominated by the bulk contribution, it is sensible to wonder if it does exist any advantageous SL for the discrimination of the other ones. With the purpose of obtaining as much as possible information on the neuron spectrum also identifying the desirable position for a spectrometer of ITER, the analysis of different SL was carried out through simulations, considering different plasma scenarios. This work is fully 49

58 presented in the paper [P3] F. Ognissanto, M. Tardocchi, L. Ballabio, G. Gorini, A. Hjalmarsson, G. Ericsson, S. Conroy, C. Hellesen, L-G. Eriksson, V. Yavorskij, V. Goloborod'Ko, Diagnostic information from non thermal neutron emission on ITER. The results of this investigation persuaded us that only the combined use of two SL brings to identify the different components in the neutron spectrum. In ITER is foreseen a set of ~40 diagnostic systems, involving machine protection, control and physics, which includes many detectors dedicated to reveal different kind of radiations: electromagnetic waves up to γ-rays, neutrons and other plasma particles. Diagnostics may be located inside the vacuum vessel and within the divertor structure, in the torus ports (fig. 3.11) and far from the tokamak. It is easily understandable that the diagnostic designs have to satisfy stringent engineering requirements, therefore also for neutron spectrometer there are difficult interface issues. This circumstance doesn t retain us to investigate the potentiality of different SL in order to reach an exhaustive knowledge of the matter and consciousness about the consequences of the constraints we are subject to. Diagnostics access Fig. 3.11: In the ITER machine 24 wall ports for diagnostic instruments will be available: 12 upper, 6 equatorial and 6 divertor ports 50

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