Seminar I b 1 st year, 2 nd cycle program Neutral beam plasma heating Author: Gabrijela Ikovic Advisor: prof.dr. Tomaž Gyergyek Ljubljana, May 2014 Abstract For plasma to be ignited, external heating is needed. Several ways of heating are known and studied. In the seminar the neutral beam plasma heating is discussed in details. High-energy neutral particles that are injected into the plasma can be produced from positive or negative ion source. For future fusion reactors neutral beams, produced by negative ion source, seem to be an effective method for plasma heating and therefore this is an important field of fusion technology research.
CONTENTS 1. INTRODUCTION... 2 2. PLASMA HEATING... 4 2.1. Ohmic heating... 5 2.2. Neutral beam injection... 5 2.3. Radio frequency waves... 6 3. NEUTRAL BEAM HEATING... 6 3.1 Generating neutral beam... 7 3.2 Optimal beam energy... 8 3.3 Negative versus positive ion source... 10 CONCLUSION... 11 REFERENCES... 12 1. INTRODUCTION Energy production is theoretically possible by both fission and fusion nuclear reactions. Since binding energy per nucleus is the largest for nuclei with mass number around 56 (Fig. 1), the energy is released when heavier atom splits into two or more smaller atoms, or when lighter atoms collide and fuse into one heavier atom. While fission reactors are commonly used worldwide, there are no commercial fusion reactors operating yet. Fig. 1: Binding energy per nucleus. [1] 2
To induce the fusion of two nuclei it is necessary to overcome Columbic force due to their positive charges and the most efficient way to supply energy is heating the fuel. At those temperatures atoms become fully ionized and the fuel is in the form of plasma. The cross section for fusion is small at low energies and it increases with increasing energy. The cross section for different reactions can vary significantly, as well as the energy at which maximum cross section is reached. Table 1 shows possible fusion reactions. Parameter E represents the energy released in specific reaction, is the largest cross section for fusion of two nuclei and is the temperature of plasma at which the is achieved. According to the table D-T reactions seem to be the most promising for future fusion reactors. Table 1: Some of the fusion reactions that can be considered for energy production. [2] Reaction E [MeV] [b] [kev] 17.59 5.0 64 3.27 0.11 1750 4.04 0.096 1250 11.33 0.16 1000 18.35 0.9 250 A high density and high temperature environment is required for fusion of two light atoms to happen and magnetic confinement is one of a very few possibilities to confine plasma, since the high temperatures would melt any material wall. First fusion experiments took place back in 1930, but it was not until 1968 that the first big break was accomplished. A group of experts in the Soviet Union developed a successful magnetic confinement tokamak, which is still the most promising type of confinement. Next important achievement was the tokamak JET. In 1997 it produced 16 MW of fusion power using deuterium and tritium, which is more than 60 % of input power. The next step in fusion research will be much larger fusion reactor ITER, followed by the first power plant DEMO. [3] For ions D and T to be fused, the ions must achieve high enough kinetic energy, therefore plasma must be heated. The main goal of fusion reactors is to produce more power from fusion than used for heating and confinement in order to be competitive with other power systems. 2. PLASMA HEATING For a plasma to be ignited, the released fusion power must overcome the power losses from Bremsstrahlung radiation and diffusion. In eq. (2.1) means fusion power density and since neutrons are uncharged and therefore the magnetic field cannot confine them, only alpha particles contribute to plasma heating. The alpha particles that are produced in D-T reactions have 3.5 MeV of kinetic energy. By colliding with other particles they transfer that energy to the plasma. Therefore so called alpha power depends on the energy of alpha particles and the rate of collisions. The rate of collisions is a function of number density of ions and electrons in the plasma ( 2.1 3
, mean relative velocity of particles and the cross section for collisions. The number density can be expressed as and the fusion power density is given as 2.2 Losses from Bremsstrahlung radiation are given as 2.3 where 2.4 and represents an effective ion charge in case where several different ions are present in a plasma. [3] Diffusion losses are power density loss because of heat flux, which leaks from a surface of plasma. It is defined as 2.5 where stands for energy confinement time. The ignition condition can be calculated from eq. (2.1) and expressed as 2.6 Losses from Bremsstrahlung are usually neglected and eq. (2.6) is simplified. 2.7 Fig. 2: Critical for ignition as a function of temperature [4]. 4
As seen in Fig. 2, the eq. (2.7) reaches the minimum at temperature 15 kev, which minimize the demands on pressure and confinement time. The external heating is needed to raise plasma temperature to about 5 7 kev. Above that alpha power becomes dominant and able to heat plasma to ignition temperature of 15 kev. External plasma heating is a complicated field that covers a broad range of types and methods. The types of plasma heating that are relevant for ITER and future fusion reactors are ohmic heating, neutral beam heating and electron and ion cyclotron heating. Further on in the seminar a neutral beam heating is discussed in details. [3] 2.1. Ohmic heating The changing magnetic fields that are used to control fully ionized plasma within the tokamak create a high intensity electrical current through induction. The current produces ohmic heating, but the resistivity of a plasma decreases with. Thus, as the plasma temperature increases, the effectiveness of ohmic heating diminishes. In typical tokamak the maximum temperature achievable by ohmic heating is about 3 kev, which is not high enough for the alpha power to dominate and sort of additional heating is required to supplement the ohmic heating. [1] 2.2. Neutral beam heating Outside of the tokamak, charged particles are accelerated with high voltage to the required energy level. Beam energy must be much higher than required plasma temperature of 15 kev. Since the charged particles cannot penetrate the magnetic field around the plasma, accelerated ions pass through an ion beam neutralizer where their electrical charge is removed. High energy beams of either neutral deuterium or neutral tritium atoms are then injected into the core of the plasma, where they are ionized and trapped by the magnetic field. The high energy ions transfer their energy as they collide with the plasma ions, increasing the plasma temperature. A disadvantage of this process is the large scale of the equipment. [5] 2.3. Radio frequency waves The energy carried by high frequency waves injected into the plasma is transferred to the charged particles, increasing their velocity. The plasma particles have different resonance frequencies (typically in the radio frequency region of the electromagnetic spectrum), depending on their mass, charge and the magnetic field strength at their location. Injecting the right frequency, a defined group of particles in a defined location can be heated selectively. The appropriate frequencies are the cyclotron frequencies of electrons (electron cyclotron heating - ECH) and ions (ion cyclotron heating - ICH), and their cyclotron harmonics. Although ECH and ICH can produce a strong absorption of energy at the center of the plasma, both methods still face technological problems. [5] 5
Fig. 3: Types of plasma heating. [1] 3. NEUTRAL BEAM HEATING Neutral beam plasma heating seems to be a promising method to achieve ignition in future fusion reactors. However, there are several problems involving both physics and technology, which must be studied before the method could be effectively used in tokamaks. One of the issues is the optimum value of the beam energy. If the beam energy is too low, it deposits most of the energy on the outside of the plasma and therefore heating will not be effective. On the contrary, if the energy of a beam is too high, the beam deposits its energy on the opposite wall, passing through the plasma with very few interactions. In current experiments beams capable of penetrating to the center of the plasma can be produced and their energy is on the order of 100 kev. However, in current experiments the density and minor radius are both much smaller than those required in a reactor. In a reactor the beam energies on the order of 1 MeV will be required to effectively heat the plasma. Neutral beams can be generated from an initial source of positive or negative ions. Present experiments mostly generate beams using positive ion sources, since the technology for producing such sources is less complicated. Efficiency is defined as ratio between beam power and input power and in the present positive ion technology it rapidly decreases with increasing beam energy, making this technology useless for future reactors. On the contrary, according to the theory the overall efficiency using negative ion sources will remain high as the beam energy increases. [4] 3.1. Generating neutral beam A neutral beam source works in in four stages (Fig. 4). In the first stage a source of lowtemperature ions are produced (usually deuterium). In the second, these ions are accelerated to high-energy by means of a high voltage. A highly directed, nearly monoenergetic beam of high-energy ions exits this stage. 6
The third stage is a neutralizer, which is a long tube filled with neutral particles of the same species as the source ions. In the neutralizer ions undergo charge exchange with the neutral particles. Positive ions undergo an inelastic collision, where a high-energy positive ion acquires an electron from low-energy neutral particle. If the high-energy ion is negative, an inelastic collision strips the excess electron from the atom. The outcome consists of highenergy neutral particles mixed with some of high-energy ions, which escaped the neutralization, and of low-energy charged particles. The final stage is a magnetic deflector that separates high-energy ions from neutral particles by magnetic field produced in the deflector region. Their energy is then collected on the beam dump. Fig. 4: Schematic diagram of neutral beam system: ion source, acceleration region, neutralizer, charged particle deflector. [5] The high-energy neutral beam can be then injected into the plasma perpendicular or parallel to the plasma axis. The first option is simpler, but particles with a large perpendicular velocity component are likely to escape the magnetic field. Parallel injection requires more beam energy because of the longer path and more complicated geometry, therefore an optimal angle of beam injection is chosen. The overall efficiency of this process can be up to 70 %, meaning that most of the energy used to produce the beam is transferred to the beam energy. [6] 3.2. Optimal beam energy Since too strong absorption leads to heating of the plasma edge and too weak absorption allows transmission of the beam through the plasma to produce heating and particle sputtering at material surfaces, the optimal beam energy is required to achieve maximum deposition of energy in the central region of the plasma. The optimal beam energy depends primarily on cross sections of various ionization mechanisms. The mechanisms of ionizing high-energy neutral particles in plasma are charge exchange, ionization by ions and ionization by electrons. In charge exchange collisions the neutral particle loses an electron to a plasma ion. 3.1 7
The subscript b in eq. 3.1 refers to high-energy beam particle and p refers to lower-energy plasma particle. The particles can be deuterium ions/neutrals as well as tritium ions/neutrals. Ionization by ions occurs when a high-energy beam particle undergoes a strong collision with a plasma. The neutral particle splits into a high-energy ion and an electron. Most of the initial energy is carried by the ion. Compared to previous two, the electron ionization has the smallest effect and therefore does not contribute much to ionization of neutral beam. 3.2 (a) (b) Fig 5: Cross section for charge exchange and ionization by ions (a) and beam penetration depths for a typical JET discharge with plasma density ( ), and a simple reactor with ( ) (b). [4] To determine the penetration depth of the neutral beam, cross sections for ionization processes need to be known. According to Fig. 5 (a) cross section for the charge exchange starts to decrease rapidly at 50-100 kev. At high-energies the ionization by ions is the dominant ionization mechanism and below 90 kev the charge exchange is the dominant one. Neutral beam flux is defined as plasma, the neutral beam decays as. When penetrating and being absorbed into the 3.3 The parameter represents the plasma density and is in general a function of distance. However, in the first approximation it is assumed to be constant. Since the loss of neutral particles means production of the same number of charged particles, the solution of eq. 3.3 is ( ) ( ) 3.4 8
and the decay length is given by 3.5 The decay length λ and penetration depth are supposed to be of the same order to heat plasma with most efficiency. In the case of perpendicular heating the beam traverses a distance of 2a (two minor radius of a tokamak) before leaving the plasma and three decay lengths are needed to reduce beam losses to an acceptably low level. The equation can therefore be written as 3.6 and the optimal energy can be determined from. In case of parallel injection the beam must propagate a longer distance and eq. 3.6 is now written as 3.7 where the parameter depends on plasma geometry. In Fig.5 (b) the eq. 3.6 is plotted for two different cases. In a reactor plasma with n = 1.5 the required penetration depth for perpendicular injection is 2 m and 6 m for parallel injection. The energies needed to achieve this penetration depths are 0.8 MeV and 3 MeV. Those energies are well beyond the range where positive ions can be used effectively and therefore negative ion sources must be developed for ITER and future fusion reactors. [4] 3.3. Negative versus positive ion source The main difference between efficiency of negative and positive ion sources at high energies is in the process of neutralization. In the case of neutralization of positive ion beams two processes need to be considered. A high-energy positive ion can exchange charge inside of neutralizer, but then it can also reionize again by colliding with a low-energy neutral particle. The number of outcoming highenergy neutral particles is therefore the number of incoming particles that only once collided with neutrals inside of neutralizer. The reactions are 3.8, 3.9 where subscript b stands for high-energy particle and n for low-energy particle. The cross sections for reactions 3.8 and 3.9 are previously mentioned and. The number of charged high-energy particles can be determined as combination of both reactions 3.10 9
If and if assumed that energy loss of high-energy beam progressing along the neutralizer is negligible, the results of eq. 3.10 are 3.11 3.12 3.13 3.14 The length of the neutralizer is typically much greater than and therefore the exponential part in eq. 3.13 can be neglected. The fraction of neutralization is defined as 3.15 In case of the negative ion beams, the analysis seems to be very similar. Negative ions can have their excess electron striped away by colliding with low-energy neutrals. Another collision can result in re-ionizing high-energy neutral particle. While the second process is exactly the same as for the positive beams, the cross section for stripping away an electron is much larger than for charge exchange because of the weak bonding of the extra electron. The reactions can be written as The fluxes of high-energy particles can be determined similar as for positive beams 3.16 3.17 3.18 3.19 In this case, after the second collision a high-energy positive ion is produced. As progressing along the neutralizer both and decay towards zero. The optimum length of neutralizer can be determined corresponding to maximum neutralization. The results of eq. 3.18 and 3.19 are 3.20 3.21 where and The neutralization fraction is 10
3.22 and the optimal length of the neutralizer is ( ) 3.23 The neutralization fraction at the output of neutralizer is therefore 3.24 Fig. 6: The neutralization fraction as function of energy for positive and negative ion beam. [4] As seen in Fig. 6, the neutralization factor for positive ion beams decreases rapidly for energies above 100 kev because of the rapid decrease of the charge exchange cross section. The optimal neutralization factor remains in order of 60 % at high energies and negative ion beams are therefore much more appropriate choice for future reactors. [4] The main reason why the negative ion sources are not in use jet is the production of negative ions. Relativelly low energy is needed to strip an electron of an atom. However, adding an additional electron to an atom is much more complicated proces and therefore much more energy is used to produce negative ions. The efficient method of producing negative is jet to be developed. CONCLUSION In an ignited plasma the -particles that are produced in D-T reactions compensate the energy losses. The fusion reaction rate strongly depends on plasma temperature. Therefore, plasma must be heated to reach the temperature of ignition. The initial heating in all tokamaks comes from the ohmic heating, caused by the torodial current. The ignition temperature cannot be reached only by ohmic heating, since the plasma resistivity decreases with increasing temperature. Therefore, some other type of external heating must be used. Neutral beam heating and radiofrequency wave heating are currently in development for future reactors. They both seem equally promising and they can be used 11
at the same time. In case of neutral beam injection, neutral particles injected into a plasma travel in straight lines, being unaffected by the magnetic field. The atoms become ionized through collisions with the plasma particles and the resulting high-energy charged particles are then held by magnetic field. Neutral beams can be generated using positive or negative ion sources. High-efficiency positive ion systems have already been developed and are used in present day research facilities. They are successful in heating experimental tokamaks, but much higher energies will be needed for future reactors and beams of those energies cannot be reached with high efficiency by this method. The high-energy neutral beam produced by technologically more complicated negative ion source seems to be an effective method to heat the plasma in a future reactor. However, the procedure is not yet fully developed and the development of this negative-ion-driven neutral beam source is an important area of fusion technology research. The first studies of neutral beam heating took place in 1973. Injections were then in order of tens of kev. Typically plasmas with temperatures of 200 ev were heated to 250 ev. By 1979 beam achieved power in order of megawatt and plasma temperature increased for several kev. Later on available beam power increased to tens of megawatt and the plasma temperatures reached tens of kev, which are in the range of reactor relevant temperatures. In the present additional studies are carried out in JET. [6] REFERENCES [1] ITER - plasma heating, http://iter.rma.ac.be/en/physics/plasmaheating/ [2] S. Atzeni, Nuclear fusion reactions, University of Oxford Press, 2004 [3] Euratom, http://ec.europa.eu/research/energy/euratom/index_en.cfm [4] Friedberg J., Plasma Physics and Fusion Energy, Cambridge university press, New York, 2007 [5] G. McCracken, P. Statt, Fusion The energy of the Universe, Elsevier Academic Press, 2005. [6] Wesson J., Tokamaks, Clarendon press Oxford, 2004 [7] EFDA European Fusion Development Agreement, http://www.efda.org/ [8] Fusion for energy, http://fusionforenergy.europa.eu/understandingfusion/ [9] World nuclear association, http://www.world-nuclear.org/ 12