Copyright. René Hartke

Transcription

1 Copyright by René Hartke 2004

2 Characterization, application and improvement of a laser driven cluster fusion neutron source by René Hartke Thesis Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of Master of Arts The University of Texas at Austin August 2004

3 Characterization, application and improvement of a laser driven cluster fusion neutron source Approved by Supervising Committee:

4 Acknowledgments For the work presented in this thesis I was supported by many people to all of whom I am deeply grateful. I have benefited from the scientific input and the helpful attitude of an amazing work group and other collaborators. First of all I want to thank Todd Ditmire. He gave me some great insights into high intensity laser matter interactions and other things. For my work he provided great physical resources. Furthermore the outstanding atmosphere in the work group is the effort of his supervising skills. Next I want to thank many people I have had the oppertunity to work with in the lab. Federico Bürsgens, Dan Symes, Gilliss Dyer, Aaron Edens, Will Grigsby, Greg Hays and Jens Osterhoff have taught me a great deal about laser treatment and have helped me to improve my laboratory skills. I also want to thank Matthias Hohenberger, Rainer Hörlein and Alexander Maltsev for some nice discussions about the theoretical background. Furthermore I want to thank Sean Keely for his assistance with the setup of the high voltage circuit. All those guys not only have helped me a lot, but also gave me a very enjoyable time. I also want to thank Roger Bengtson and Keith Carter who provided me with high voltage parts and great suggestions for high voltage and vacuum related problems. In addition to that Roger Bengtson was so kind to act as the co-reader for my thesis. I am very grateful to my parents and my sister who encouraged me to study iv

5 abroad. Since I can remember I could always count on their support and motivation. For this and many other things I owe a great debt to them. René Hartke The University of Texas at Austin August 2004 v

6 Characterization, application and improvement of a laser driven cluster fusion neutron source René Hartke, M.A. The University of Texas at Austin, 2004 Supervisor: Todd Ditmire The explosion of deuterated clusters heated by ultra short, high intense laser pulses provides ions with sufficient energy to undergo fusion reactions. Based on this mechanism monochromatic dd-fusion neutrons can be produced by illuminating deuterium clusters with a high intensity laser. For the work presented in this thesis we employed such a cluster fusion neutron source. The clusters from a cryogenically cooled gas jet were heated with a femtosecond, terawatt class Ti:sapphire laser. The results presented in this thesis fall into three categories. First general features of the neutron source will be discussed including the energy dependence and the angular dependence of the neutron source. Then as a first application of the source the calibration of a neutron detector for single shot dd-fusion experiments will be presented. Finally magnetic confinement as a method for increasing the neutron yield will be discussed. vi

7 Contents Acknowledgments Abstract List of Figures iv vi x Chapter 1 Introduction 1 Chapter 2 Laser Cluster Interactions The Ponderomotive Potential Ionization Processes Multiphoton Ionization Tunnel Ionization Barrier Suppression Ionization The Keldysh Parameter Plasma Heating Above Threshold Ionization (AT I) Collisional Heating Cluster Formation Requirements and Simplifying Assumptions for Plasma Treatment of Clusters vii

8 2.6 Cluster Explosions Cluster Expansion Ion Energies Neutron Yield Calculations Expected Angular Distribution Chapter 3 Apparatus for Cluster Experiments The Laser System The Target Chamber Cluster Production Diagnostics Chapter 4 Characteristics of the Cluster Neutron Source Cluster Size Measurements Time of Flight Histograms Pressure Dependance of the Neutron Yield Energy Dependance of the Neutron Yield Polarization Scan Angular Distribution of the Neutron Yield Conclusions Chapter 5 Calibration of a Neutron Detector The Sandia Z Accelerator The Neutron Detector on Z Calibration Data Conclusions Chapter 6 Pulsed Magnetic Mirror Confinement of the Plasma Filament 58 viii

9 6.1 Confinement of the Plasma Filament Creating a High Magnetic Field Design of the Circuit Results Conclusions Chapter 7 Conclusions and Future Directions 65 Bibliography 68 Vita 75 ix

10 List of Figures 2.1 Multiphoton ionization Atomic potential, distorted potential and barrier suppression ATI vs inverse bremsstrahlung Comparison of the total energy distribution with a Maxwellian Mechanism of fusion from exploding clusters Illustration of the cluster target Fusion yield scaling Fusion contributed from the Maxwell tail Differential cross section for the 2 H(d, 3 He)n reaction Overview of the THOR-laser Schematics of the target chamber Gas-jet with supersonic nozzle Photo of target chamber Pressure scaling of Rayleigh scattering signals Temperature scaling of Rayleigh scattering signals Time of flight histogram Pressure dependence of the fusion neutron yield Energy dependence of the fusion neutron yield x

11 4.6 Polarization dependence of the fusion neutron yield Angular distribution of the neutron yield Schematics of the Z-machine at Sandia National Laboratories Schematic illustration of a z-pinch driven hohlraum Position of the detector Schematics of the detector design Schematics of the setup for the calibration Time of flight histogram for detector calibration Histogram of peak areas Average pulse heights at different bias voltages Schematics of magnetic mirror confinement Illustrated circuit Schematics of laser triggered spark gap Test circuit for B-field formation Simulation of the maximum B-field Schematic illustration of the setup for a rotating plasma filament.. 66 xi

12 Chapter 1 Introduction The development of Chirped Pulse Amplification (CPA) [1] opened the way for studies with ultra short, high intense laser pulses on table top lasers. Compact laser systems providing peak powers of several terawatts are now available in many laboratories where it is possible to generate focussed intensities of > W/cm 2. At such intensities the laser electric field becomes comparable to the electric field felt by an electron in an atom. The physics of laser-matter interactions accessed a new regime where atoms could be ionized almost instantaneously by intense laser fields. In particular the interaction of femtosecond lasers with atomic clusters now is a field of high interest [2, 3, 4, 5], because it was observed that lasers very efficiently couple into cluster gases [6] whereas the absorption in gases at near atmospheric pressure is very ineffective. This is due to the different heating mechanisms in both cases and will be explained later in this thesis. Clusters are accumulations of atoms bound together by van-der-waals forces. They form during the expansion from a high pressure reservoir vacuum through a nozzle. Atoms in clusters that are illuminated by an intense, ultra short laser pulse 1

13 get ionized. Electrons leave the cluster and the ionized cluster expands due to Coulombic repulsion of the positive charged atoms. Depending on the ionization time, which in turn depends on the intensity of the pulse and the pulse duration, either the expansion of the partially stripped cluster or the full ionization is going to happen faster. In the first case the cluster expands hydrodynamically whereas in the latter case it Coulomb explodes [7]. For the Coulomb explosions the ions can gain energies of many kev. A fundamental fragment of the interest in laser-cluster interactions concerns clusters of deuterium or lately also clusters formed from deuterated heteronuclear molecules. Upon irradiation with a short, intense laser pulse, a gas of deuterium clusters can exhibit extremely efficient deposition of energy creating a plasma with energy densities reaching 10 5 J/cm 3 [8]. The instantaneous ejection of almost all electrons from the clusters results in a Coulomb explosion of the clusters in which the ions gain sufficient energy to undergo dd-fusion [9, 10]. In 50 % of the fusion events a characteristic 2.45 MeV neutron will be emitted: D + D T (1.01MeV ) + p(3.02mev ) D + D He 3 (0.82MeV ) + n(2.45mev ) Both reactions have about the same probability. Hence the irradiated clusters act as a reliable pulsed source for energetic, monochromatic neutrons. Such a table-top neutron source utilizing pure deuterium clusters was first presented by Ditmire et al. [4]. This method for producing fusion neutrons is very attractive due to its high repetition rate, its inexpensive and compact design and its easy handling. In addition, the neutron burst is ultra-short [11] and scales favorably with increasing laser pulse energy [12]. 2

14 Various other methods for neutron generation from laser-produced plasmas have been demonstrated over the past few years [13]. Neutrons can be generated in a secondary process where nuclear reactions occur in a sample material irradiated by energetic electrons or radiation produced in the plasma. This process was suggested as a possible basis for a neutron source by Schwoerer et al. who used the radioactive decay of the sample as a means of measuring hard x-ray yields [14]. Using large scale laser systems, with focussed intensities exceeding W/cm 2 it is even possible to carry out nuclear physics experiments and to cause photoinduced fission of 238 U [15, 16]. The great interest for fast (MeV) neutrons relies on the various applications especially in material science. In advantage to the high fluxes provided by accelerators, plasma pinches or spallators that typically yield neutron pulses with durations greater than a few nanoseconds [17], laser driven fusion plasmas can produce short bursts of fast neutrons [11]. These short-pulse neutron sources open the possibility of ultra fast (subpicosecond) studies for example of the material damage by neutrons [18, 19]. Such tests are particularly important for the construction of fusion reactors. Other applications can be adopted in radiography [20]. Furthermore the use of facility-scale laser systems to achieve energy producing fusion has been the goal of laser interaction experiments for many years [21, 22, 23]. Neutron yields have been measured from both a gaseous deuterium medium [24] and deuterated plastic targets [25]. The neutron yield of a cluster fusion source crucially depends the conditions of the experiment like the cluster size, the laser intensity or the target density. Cluster fusion sources are capable of yields up to 10 5 fusion neutrons per Joule of incident laser energy using deuterium clusters [4]. Grillon et al. demonstrated that 3

15 even higher ion energies can be achieved from deuterated methane clusters [26]. This should lead to higher fusion yields due to an increased cross section [27, 28]. In this thesis we will present an experimental result for the dependance of the neutron yield on the laser energy as well as on the angle of emission. This investigation is aimed to characterize the physics of the plasma filament that emits the neutrons. As a first application of the fusion neutron source we employed it to calibrate a high sensitivity neutron detector [29] designed for operation on experiments performed on the Z facility [30, 31] at Sandia National Laboratories. Typically, the detector will be used in single shot dd-pellet ignition [32] experiments in which a relatively small neutron signal must be distinguished from a strong flux of bremsstrahlung radiation. The cluster fusion neutron source satisfies all the important demands for this calibration. Monochromatic 2.45 MeV neutrons, which primarily will be observed with this detector, are supplied at a high repetition rate and good statistics can be achieved. The calibration profits from the low flux of bremsstrahlung emitted by this source. Furthermore femtosecond laser driven pulsed neutron sources are of particular interest for material studies, because they provide the opportunity to image the neutron damage on a femtosecond time scale. But for material damage experiments with neutrons much higher fluxes than provided by any known table-top laser driven source are required. In this thesis we propose a method where the plasma filament is confined by a magnetic mirror. This will counteract the expansion of the plasma so that the ion density will not decrease that rapidly. For such a confinement fields of about 200 Tesla are required. The magnetic field for the confinement will be 4

16 generated by miniature coils next to the plasma. The purpose of this thesis is to characterize experimentally the cluster neutron source and to propose a way to improve its yield for further applications. Also a method for the calibration of a neutron detector is described. The structure of this manuscript is as follows. In the next chapter we will provide the theoretical background for the work that is issued in this thesis. This includes a description of the ionization of clusters and the prevailing heating mechanisms. In chapter 3 the setup of the experiment for cluster fusion studies is described. The presentation of results begins in chapter 4 with the characterization of the cluster neutron source. In chapter 5 the calibration of a neutron detector for use on Z at Sandia National Laboratories is described. A method for increasing the neutron yield of the source is presented in chapter 6. This includes the description of a electric circuit that generates a high magnetic field. Chapter 7 summarizes the results of this work and discusses potential directions and applications for this experiment. 5

17 Chapter 2 Laser Cluster Interactions The purpose of this chapter is to introduce some of the basic concepts that describe the interaction of intense, short laser pulses with atoms and clusters in a gas. The following chapters will presume the background introduced here. 2.1 The Ponderomotive Potential The oscillation of a strong laser electric field can drive an electron. The equation of motion for an electron oscillating in free space in the absence of an atomic ion can be written as m e ẍ(t) = ee 0 sin ω 0 t (2.1) where m e is the electron mass, e is the electron charge, E 0 is the peak electric field and ω 0 is the laser frequency. From the oscillating laser field the electron acquires a kinetic energy of 1 2 m ev(t) 2 = e2 E0 2 2m e ω0 2 cos 2 ω 0 t (2.2) 6

18 The cycle averaged kinetic energy of the electron is the quiver or ponderomotive energy of the electron U pond = 1 2 m e v 2 = e2 E 2 0 4m e ω 2 0 (2.3) The ponderomotive energy at an intensity of W/cm 2 for laser light with a wavelength of λ = 1 µm is 1 kev. 2.2 Ionization Processes Multiphoton Ionization At high intensities photo-ionization can occur even if the photon energy is below the ionization potential of the atom. An atom can gain sufficient energy by absorbing more than one photon before the excited electron decays back to the ground state. This process is called multiphoton ionization. Fig. 2.1 shows a schematic picture of this mechanism. Figure 2.1: Schematic of multiphoton ionization. An atom can be ionized by absorbing more than one photon. 7

19 This picture is good until the laser strength becomes comparable to the atomic field strength. This strong field begins with laser intensity of roughly W/cm 2. The actual ionization regime for a particular experiment can be determined using the Keldysh parameter, which will be introduced later Tunnel Ionization For higher intensities the laser electric field is strong enough to distort the atomic potential (Fig. 2.2). At this point the effects on the Coulomb potential can not be treated as perturbations anymore. A quasi-classical picture of an electron trapped in the potential well of an atom gives a better agreement here. If the distortion is strong enough, the electron can tunnel through the barrier, a process called tunnel ionization. A general relation for the tunneling rate of a complex atom has been worked out by Ammosov, Delone and Krainov [33]. The so-called ADK-rate has been derived by averaging the tunneling rate over a single optical cycle W tunnel = ω a (2l + 1)(l + m )! 2 m m!(l + m )! ( 2e n )n I P 2E ( π(2i P ) 3/2 )1/2 ( 2(2I P ) 3/2 ) 2n m 1 exp[ 2(2I P ) 3/2 ] E 3E (2.4) where ω a is the atomic frequency, l and m are angular momentum quantum numbers, n is the effective principal quantum number, I P is the ionization potential of the particular charge state and E is the laser electric field Barrier Suppression Ionization As the laser intensity increases even further, the barrier gets suppressed below the ionization potential of the atom. At this point the ionization rate becomes significant. The effective potential seen by an electron in a Coulomb potential with 8

20 Figure 2.2: a) The electron wavepacket is bound by the Coulomb potential of the atom. b) For a laser distorted atomic potential the wavepacket has a probability to tunnel through the barrier. c) The barrier can be suppressed below the electron potential for sufficient strong laser fields. 9

21 an external field E 0 is V (r) = Ze2 4πɛ 0 r ee 0r (2.5) By setting the first derivative equal to zero we get the radius for which the barrier has its local maximum: V r = r max = Ze2 4πɛ 0 r 2 ee = 0 Ze 4πɛ 0 E 0 (2.6) To calculate the required electric field which is sufficient to suppress the barrier, we set the effective potential at r = r max equal to the ionization potential of the atom: where I P E 0 = I2 P πɛ 0 Ze 3 (2.7) is the ionization potential of the atom. The laser intensity is given as I = cɛ 0 2 E 0 2, where c is the speed of light. Therefore the corresponding intensity is I 0 = ci4 P π2 ɛ 3 0 2Z 2 e (I P [ev ]) 4 Z 2 [ W cm 2 ] (2.8) From this equation the intensity for which the ionization rate becomes reasonable can be estimated easily. Hydrogen (I P = 13.6 ev ), for example, will ionize at an intensity of W/cm 2. From this relation the appearance intensity of a particular charge state by tunneling can be estimated. The results from this model are in good agreement with the ADK tunnel ionization rate The Keldysh Parameter A good criteria to determine which ionization process dominates during the experiment is the Keldysh parameter. It is defined as I P γ = = ω (2.9) 2U pond ω tunnel 10

22 where ω is the laser oscillation frequency and ω tunnel is the tunnel ionization frequency. When the tunneling frequency exceeds the laser frequency, the tunnel ionization will predominate. In the other case multiphoton ionization will be the dominating mechanism. For the work presented in this thesis we used laser intensities of about W/cm 2, which corresponds to a Keldysh parameter of γ 0.01 for deuterium. Hence we are certainly in the tunneling regime. 2.3 Plasma Heating Several competing mechanisms are responsible for the coupling of laser energy into a solid density plasma. Typically the energy is primarily transferred to the electrons due to their lighter mass. By collisions or space charge effects the electrons then accelerate the ions. Only heating mechanisms that are relevant for gaseous, optically ionized plasmas illuminated by short laser pulses are considered here Above Threshold Ionization (AT I) Since we assumed that the primarily ionization process for the work we present in this thesis is tunneling ionization, we can reduce the discussion of ATI to this regime. ATI occurs, if an electron is ionized at a phase that is shifted by ϕ > 0 from the peak of the laser electric field. The additional photon energy will than increase the electron kinetic energy by E kin,at I = 2U pond sin 2 ϕ (2.10) For ϕ = 0 the electron will not have gained any energy after the laser pulse has passed, because the average acceleration will be zero. Since the probability of tunnel 11

23 ionization is highest at the peak of the E-field, we expect the majority of electrons to ionize close to ϕ = 0 for a linearly polarized field. The ATI energy will be small compared to the ponderomotive potential. Therefore ATI is an ineffective coupling of energy into a plasma Collisional Heating Collisional heating is also known as inverse bremsstrahlung heating. electron that is accelerated by an incoming laser pulse will have the same energy as before, once the electric field has returned to zero. This changes if the electron undergoes collisions with ions while it is still accelerated. For example, if the electron undergoes a 90 collision that occurs instantaneously, it loses all its velocity in the direction of the e-field and maintains energy after the pulse has passed. An estimation of the heating rate can be made assuming that the electrons contribute their peak energy to the plasma upon every collision. The collision frequency is where dσ dω An ν ei = dσ dω vn if(v th )dv th (2.11) is the differential coulomb velocity cross section, v is the electron velocity (given as the sum of the thermal velocity and the oscillatory velocity u(t) = u 0 sin ωt), n i is the ion density and v th is the thermal velocity. To obtain the heating rate we have to average over all possible scattering angles and over a whole laser cycle. We get the cycle averaged energy deposited per unit time dw dt = n i 2f(v th )dv th Z 2 e 4 m e 1 u 0 ln Λ ln u 0 v th for u 0 > v th (2.12) where ln Λ is the coulomb logarithm. For u 0 < v th the heating rate is zero. The optimum collisional heating rate occurs if the oscillating velocity is comparable to the thermal velocity. This means that the thermal velocity of the electrons gets comparable to the ponderomotive energy of the pulse. To achieve this result we had 12

24 to assume that all collisions are elastic and that the collision time is small to one cycle of the oscillation. Figure 2.3: Schematic heating rate for ATI and inverse bremsstrahlung for U pond = W/cm 2. For small intensities ATI is the prevailing mechanism and for high intensities inverse bremsstrahlung dominates. When a cluster plume is illuminated by an intense laser, field ionization sets free initial electrons immediately, forming a high density plasma ball. Because of the high electron ion scattering rate in this dense plasma, heating by inverse bremsstrahlung dominates over ATI. As can be seen from Figure 2.3, this is much more effective. Therefore laser absorption is significant enhanced for cluster gases compared to atomic gases. 2.4 Cluster Formation According to the ideal gas law, a gas that adiabatically expands from a high pressure reservoir into vacuum cools down. The cooling causes the gas to condensate 13

25 and clusters form. This effect can be enhanced by directing the gas by a nozzle such that the relative velocities of the particles in the gas get drastically reduced. The efficiency of this process, and hence the size of the formed clusters, depends on the backing pressure P 0 in the reservoir, the initial temperature T 0, the geometry of the nozzle and the kind of gas used. The onset of cluster formation as well as the size of clusters produced can be described by the empirical scaling parameter referred to as the Hagena parameter [34] Γ = k (d/ tan α)0.85 P 0 T (2.13) where α is the expansion half angle, d is the orifice diameter of the nozzle and k is a constant related to the inter-molecular bonding potential of the clustering gas (e.g. k = 184 for hydrogen). Cluster formation is a statistical process. Usually the distribution of cluster sizes is relatively broad. Gas jets with the same Γ form clusters of about the same average size. For the regime of large clusters (> 10 3 atoms/cluster) the average number of atoms per cluster N C approximately scales as N C Γ 2.0 (2.14) A convenient method of measuring the cluster size is optical Rayleigh scattering. An interesting property of cluster media is, that they have the average density of a gas whereas the single clusters have a near solid density. 2.5 Requirements and Simplifying Assumptions for Plasma Treatment of Clusters To describe the mechanisms of laser cluster interactions we treat the illuminated clusters as a plasma. In the following we want to justify this model and make some assumptions for the sake of simplicity. 14

26 A plasma treatment is only valid if quasi-neutrality is ensured for the ambit of the cluster. Hence the majority of ionized electrons have to be confined to the cluster for the duration of the laser pulse. This is given for large clusters (> 1000 atoms/cluster) where, like it is the case for a solid, the majority of electrons are confined by the space charge. Plasmas can shield out electric potentials that are applied to it. An electric charge in a plasma attracts particles of the opposite charge that almost immediately form a cloud around it. If there were no thermal motions (cold plasma), the isolation would be perfect and no electric field would be present in the plasma outside the clouds. For a finite temperature particles at the edge of the cloud can escape the electric potential. The radius where the potential energy of these particles equals their thermal energy is called the Debye-length [35] ɛ0 kt e λ D = ne 2 (2.15) where k is the Boltzmann constant, T e is the electron temperature, n is the electron density and e is the electron charge. A criterion for an ionized gas to be a plasma is that it has to be dense enough such that the dimension of the cluster is much larger than the Debye length. For typical parameters in our experiments the Debye length is < 1 nm whereas the cluster diameters are in a range of 3 10 nm. Hence the criterion is fulfilled. The third requirement is that that the cluster has to hold together on the time scale of the laser pulse in order to interact with it. Assuming sound speed an expansion to of the initial density would take about 1 ps. Since the work was done using femtosecond laser pulses this requirement is clearly satisfied. To simplify the following calculations we assume the plasma to be spherical. Furthermore it is assumed that all particles in a cluster experience the same laser electric field strength. This is valid since the cluster diameter is much smaller than 15

27 the laser wavelength and the plasma skin depth. The ion density distribution is assumed to be uniform across the cluster and the expansion is assumed to be selfsimilar so that the electron density remains uniform throughout the expansion. Another assumption is that the temperature distribution across the plasma is isotropic. 2.6 Cluster Explosions Cluster Expansion The characteristic velocity for a plasma expansion is the plasma sound speed γzkte c s = (2.16) m i where m i is the ion mass and γ is the adiabatic index (γ = 3 5 for ideal gas). There are two mechanisms that drive the cluster expansion. The repulsion between the ions after a charge build-up on the cluster results in a Coulomb pressure P Coulomb = Q2 e 2 8πr 4 (2.17) where Qe is the charge build-up and r is the radius of the cluster. The thermal motion of the hot electrons leads to a hydrodynamic pressure P Hydrodynamic = n e kt e (2.18) Notice that the scaling with the cluster radius is r 3 in the hydrodynamic case (since n e vol 1 ) and r 4 in the Coulomb case. Hence the hydrodynamic case gets more important for larger clusters. For the intermediate regime of those two cases a calculation for the equation of motion of electrons in a uniform spherical cluster was done by Breizman and Arefiev [36]. For this work only the regime of Coulomb explosions is of interest. Intensities such as provided by the THOR-laser are sufficient to ionize D 2 or CD 4 clusters with 16

28 a diameter of a few nanometers within a few laser cycles. discussions will be restricted to this case. Hence the following Ion Energies Like discussed earlier, electron-ion collision heat up the electrons efficiently. But due to the extremely small disassembly time of the plasma filament [10], there is insufficient time for the electrons to transfer their energy to the ions through collisions. Instead the ions gain energy through Coulomb explosion. The maximum energy for ionized clusters is given by the potential of the outermost ions E max = q n ie 2 r 2 3ɛ 0 (2.19) where q is the average charge state in the cluster, n i is the initial ion density and r is the cluster radius. The disassembly time is defined by the time required for a uniformly charged sphere to grow to twice its initial radius [10] and for deuterium clusters given by 4πɛ0 m D t dis 0.8 n i e 2 (2.20) where m D is the mass of a deuteron. For a typical deuterium cluster density this time is 20 fs. If the rise time from initial ionization intensity to an intensity sufficient to remove the majority of electrons in the cluster is comparable to the disassembly time, the cluster will explode while the charge density is maximum. For significantly larger rise times or lower peak intensities, the cluster will start to expand before all electrons are removed and the charge density will be reduced. Hence we need ultra short laser pulses and high peak intensities to convert the maximum electrostatic energy into ion kinetic energy. The Coulomb explosion isotropically accelerates the deuterium ions to substantial energies, but only the surface ions acquire the maximum energy. The full 17

29 energy distribution is given by f(e)de = A EdE (2.21) where A is a normalization constant and E > E max. This distribution is shifted towards high energies and the average energy is equal to 3/5 E max. The peak energies can be up to a few tens of kev. This is sufficient to give them a significant probability for dd-fusion when colliding with ions from nearby clusters. The ion energy distribution above is only valid for single cluster explosions. Relying on previous studies [37] we assume a log-normal distribution for the cluster sizes for our gas jet. The density for clusters of the size N can be written n C (N) = n C,total Nσ N µ)2 exp( (ln 2π 2σ 2 ) (2.22) where µ and σ are the mean and standard deviation and N is the number of molecules or atoms in a given cluster. The energy distribution for such an ensemble of Coulomb exploding clusters is f(e)de g(e) EdE (2.23) where g(e) is given by g(e) = and N E is a cluster size related to E. N E n C (N)dN (2.24) The total energy distribution given by the convolution of the cluster size distribution with the energy distribution for single clusters is almost Maxwellian as can be seen from Figure

30 Figure 2.4: Calculated total energy distribution. It is a good approximation to assume the ion energy distribution to be Maxwellian. 2.7 Neutron Yield Calculations Deuterium ions from neighboring exploding clusters can have sufficient kinetic energy to undergo fusion processes. The underlying principle of this mechanism is illustrated in Figure 2.5. For various application of the cluster source a high neutron yield is required. Therefore we are interested in predicting the yield for various configurations. For sake of simplicity we will only look at pure deuterium clusters. The beam target consists of a hot plasma filament surrounded by a cold ion plume. If two deuterium ions approach each other to a sufficiently small distance, fusion occurs. This is only possible for high kinetic ion energies. The possible dd-fusion processes are described by the reactions D + D T (1.01MeV ) + p(3.02mev ) 19

31 Figure 2.5: Schematic illustration of the mechanism for nuclear fusion from exploding deuterium clusters. The laser irradiated clusters Coulomb explode and create plasmas with sufficient ion energies for substantial nuclear fusion. D + D He 3 (0.82MeV ) + n(2.45mev ) Both reactions have about the same probability, hence in every second fusion reaction a neutron is produced. To calculate the yield we have to look at two different regions for neutron production. The fusion processes can either happen from collisions of two hot electrons in the filament or from collisions of hot ions that leave the filament with cold ions in the plume. The total yield is the sum of both processes. For the fusion yield inside the plasma filament an approximation is given by the expression Y filament τ dis 2 n 2 i σv dv (2.25) where τ dis is the disassembly time of the plasma filament, σv is the velocity averaged fusion cross section and V is the initial volume of the plasma. A factor of

32 Figure 2.6: Illustration of the cluster target. The laser hits the beam target 2 3 mm below the nozzle. Fusion neutrons can be produced in the plasma filament and in the cold surrounding plume. is included in this expression to account for the indistinguishability of the two ions that collide. Moreover the plasma disassembly time τ dis reflects that the fusion yield from the filament also depends on the ion density. The contribution from reactions in the plume is Y plume N i σ v dl (2.26) where N i is the number of ions leaving the filament and σ v is the fusion cross section for the plume. Whereas in the first case the cross section is weighed by the ion velocities given by a Maxwellian distribution, the cross section for the plume refers to an individual ion velocity v hitting a particle at rest. Since the probability for fusion events is comparably low, the contribution from the plume is minor. For this reason we limit the further discussion to fusion events in the hot filament. 21

33 For the temperature dependance of the fusion cross section σv, an empirical expression is given by [38] σv DD [ cm3 s ] T 2/3 [kev ]e T 1/3 [kev ] (2.27) which was verified by experimental data for temperatures below 25 kev. The plasma disassembly time can be given by τ dis = γ V 1/3 v (2.28) where γ is a dimensionless geometrical factor, V is the volume of the plasma filament and v is the average ion velocity given by v = 16Ēi 3πm i (2.29) We now assume, that the laser energy is completely absorbed in the plasma. Hence the average ion energy Ēi equals the laser energy divided by the initial number of ions E laser = NĒi = V n i Ē i = V n i 3 2 k BT V = E laser n i 3 2 k (2.30) BT Using equations (2.29) and (2.30) we can now rewrite the plasma disassembly time in known quantities τ dis = γ V 1/3 v = γ( E laser 3/2k B T n i ) 1/3 γe 1/3 laser = m1/2 i k bt/3πm i n 1/3 (2.31) i (k B T ) 5/6 To solve the integral we make the assumption that not only the ion density, but also the temperature and therefore the fusion cross section are constant over V. Using (2.27) and (2.31) we find the fusion yield to be Y γ E 4/3 laser m1/2 i n 2/3 σv i (k B T ) 11/6 (2.32) 22

34 As we can see from Figure 2.7 the fusion yield has a maximum at T = 15.6 kev. Left of the maximum the yield rises due to the positive slope of the fusion cross section. At the maximum the effects from a decreasing disassembly time starts to dominate and the yield decreases. Figure 2.7: Calculated fusion cross section a) and fusion yield scaling b) as a function of ion energies. The fusion cross section grows steadily with higher ion energies. The fusion yield scaling reaches its maximum at T = 15.6 kev (F. Buersgens [39]). A typical ion density in a deuterium cluster plume is n i = cm 3 [4]. To make an upper bound calculation we assume the optimum average ion energy of 24.4 kev. Furthermore we use the value of the local maximum for the fusion cross section. This gives us the upper bound of the fusion yield that only depends on the 23

35 laser energy and a geometric factor Y γ E 4/3 laser (2.33) The fusion yield is twice the number of the neutron yield, because only every second dd-fusion reaction releases a neutron. Compared with recent neutron yield measurements [12] this result turns out to be slightly overstated. 2.8 Expected Angular Distribution One of the observations we present in this thesis concerns the angular distribution of the neutron yield. In this section we will go into the details of some mechanisms happening in the beam target. As we can see from Figure 2.8 most of the fusion events emanate from collisions of ions in the high energy tail of the Maxwellian distribution. The steep increase of the fusion cross section overcompensates the relative small number of ions. R. Brown et al. [40] measured the differential cross section for the dd-fusion reactions with high precision for ion energies > 20 kev. Since only about 3% of the fusion events are caused by ions with lower energies than 20 kev, we can use their results for calculating the differential cross section for the cluster fusion source. Brown et. al studied the differential cross section for the center of mass system (cm). To account for the motion of the center of mass system we have to convert their result to the laboratory system (l) σ l (θ l, φ l ) = (1 + γ2 + 2γ cos θ) 3 σ cm (θ cm, φ cm ) (2.34) γ cos θ where γ is a coefficient given by the ratio of the speed of the center of mass in the laboratory system to the speed of the observed particle in the center of mass system. 24

36 Figure 2.8: Calculated fusion yield contribution of Maxwell distributed ions as a function of ion energy. For an average ion energy of T = 12 kev more than 97 % of the fusion events result from ions with energies of 20 kev and more (F. Buersgens [39]). Based on geometric considerations γ is found to be m 1 m 3 E γ = m 2 m 4 E + Q (2.35) where Q is the energy released by the nuclear process and E is the energy initially associated with the relative motion in the center of mass system. In Figure 2.9 the differential cross section is shown for the fusion reaction that yields neutrons and an initial ion energy of E l = 20 kev. From Figure 2.9 we see that the differential cross section is higher in forward and in backward direction. This can be explained with the conservation of momentum. The energy of the ion hitting a particle at rest is much bigger than the energy of the released neutron. Therefore the neutron has to fly away essentially along 25

37 Figure 2.9: The green curve shows a fit of the differential cross for the collision of a deuteron with an energy of 20 kev with a deuteron at rest for the center of mass system experimentally observed by Brown et. al [40]. The red curve shows the same fit converted to the lab system (F. Buersgens [39]). the axis of collision. The fact that the anisotropy increases for higher ion energies substantiates this explanation. With this background we are capable of making a prediction for the angular distribution of neutrons. Almost all of the neutrons emerge from collisions of hot ions in the plasma filament. The extension of the filament is much longer in the direction of the laser axis then perpendicular to it. Hence the majority of collisions will happen along the laser axis. In combination with the differential cross section we therefore expect a distribution with a higher yield along the laser axis. 26

38 Chapter 3 Apparatus for Cluster Experiments 3.1 The Laser System All experiments presented in this thesis were performed on the THOR-laser system. The Texas High-Intensity Optical Research facility is a multi terawatt table-top laser system providing 40 fs pulses with energies of up to 0.6 J at a wavelength of 800 nm. The repetition rate is 10 Hz. THOR is based on the concept of chirped pulse amplification (CPA) [1]. This means that an ultra short pulse gets stretched in time before being amplified and compressed again. CPA is required to avoid dangerously high intensities during amplification. The desired unfocussed intensity for a terawatt laser is > W/cm 2 which is high enough to damage optics. Furthermore at such intensities the materials in the laser chain have a nonlinear index of refraction. Hence self-focussing, for example of perturbations on the beam, can cause damage in long amplifier rods. CPA successfully deals with these problems by dramatically reducing the intensity of the pulse in the amplifier chain. 27

39 Figure 3.1 shows the schematics of the THOR laser system. In the Ti:sapphire oscillator a 20 fs, 6 nj pulse is created by achieving a fixed phase relation for various cavity modes with different wavelengths (mode-locking). This pulse with a center wavelength of 800 nm has a relatively broad spectrum of 30 nm full-width at half-maximum (FWHM). By a diffraction grating the spectrum of the pulse gets dispersed and the following optics are arranged such that for shorter wavelengths the optical path becomes longer than for longer wavelengths. The pulse gets stretched in time and the pulse coming out of this stretcher has a duration of 600 ps. Consequently the intensity is reduced by a factor > 10 4 and can safely be amplified. Figure 3.1: Overview of the THOR-Laser. In three amplification stages the beam gains a maximum energy of 1.2 J before being compressed to about 40 fs. The spectrum for the stretched pulse, which normally is in the infrared, is sketched as a visible spectrum. 28

40 The pulse gets boosted in three different amplification stages. They all contain Ti:sapphire crystal as amplifying medium. The main advantage of this material is its broad tunability which is required for the wide spectra of chirped pulses. It also provides a large gain cross section and good thermal diffusivity. On the other hand the relatively low saturation level and the short upper state lifetime limit the output energy and the repetition rate. Coming from the stretcher the pulse is injected into a regenerative amplifier. In this cavity it gets amplified to about 2 mj by passing a Nd:YAG laser pumped Ti:sapphire crystal. The gain that can be achieved in each stage is limited by the saturation fluence of the crystal (0.8 J/cm 2 for Ti:sapphire). In the regenerative amplifier saturation is reached after about 30 passes and the pulse is switched out by a high-speed pockels cell at that point. In order to obtain higher energies, the aperture of the seed pulse now is increased from 2 mm to about 4 mm before it reaches the next amplifying stage. In the four-pass the beam is guided through a bow-tie shaped array of optics that has a Ti:sapphire crystal in the middle. The pulse passes this crystal, which is pumped by the same laser as the regenerative amplifier, four times. The energy after the four-pass is > 20 mj. The final amplification happens in a five-pass amplifier. Two q-switched 1.4 J Nd:YAG lasers pump a 20 mm diameter Ti:sapphire crystal. By intentionally mistiming the pump pulses with respect to the seed pulse, the output energy of the five-pass can be varied over a range of 6 mj 1.2 J. After amplification a vacuum spatial expands the beam to its final aperture of 50 mm. In a single grating pulse compressor the pulse duration gets compressed to 40 fs by reversing the effects from the stretcher. The optical path for smaller wavelengths now is shorter and the geometry of the compressor is designed such that the differences in pathlengths from the stretcher are exactly compensated. However 29

41 the initial pulse duration of 20 fs can not be achieved anymore. One reason for this is that it is impossible to compensate all dispersion effects that the pulse experiences in the various optics it passes during amplification. Therefore the pathlengths through the whole assembly of stretcher, amplifier and compressor will always be slightly different for different wavelength. In addition to this mechanism the spectrum narrows during amplification because the gain in the Ti:sapphire crystals is lower for the edges of the spectrum, an effect that is called gain narrowing. Owing to Heisenberg s uncertainty principle a narrowed spectrum corresponds to a longer pulse. 3.2 The Target Chamber All experiments were performed in a vacuum chamber that is connected to the compressor by a vacuum transport. The laser beam is guided from the compressor to a switchyard, were it is redirected to this chamber. At this point the diameter of the beam is 5.0 cm. The geometry of the main elements in the chamber is shown in Figure 3.2. The beam first hits a mirror that reflects it in an angle of 3.2 to a spherical mirror. This f/10 optic focusses the beam under the nozzle of the gas jet. The focal spot size can be assumed to be approximately 60 µm, which corresponds to an maximum intensity of > W/cm 2. This already accounts the losses in beam energy of almost 50 % on the light pass from the final amplification stage to the target chamber. Most of those losses occur during compression. With a X-Y-Z stage the gas jet can be shifted in the optimum position for each experiment. It is typically positioned in the center of the chamber. For polarization experiments a λ/2 waveplate can be integrated into the beam pass. With a clear aperture of 47 mm it reduces the beam energy by a small amount. The wave- 30

42 Figure 3.2: Schematic of the target chamber. The laser enters the chamber from top right. A spherical mirror focusses the beam under the gas jet. plate can be rotated from outside of the vacuum to change the laser s polarization. 3.3 Cluster Production For cluster production a gas jet with a high backing pressure is used. Typically the gas is compressed to 1000 psi. The gas is cryogenically pre-cooled in a reservoir in the gas jet. For this purpose nitrogen is guided through the coolant pipes that surround the gas jet. For the case of deuterium clusters the gas has to be cooled 31

43 down to a temperature close to the condensation point of N 2, for deuterated methane clusters the temperature is typically close to the freezing point of water. Figure 3.3: Schematics of the gas-jet with supersonic nozzle. (R. A. Smith et al. [41]) The opening of the gas jet is controlled by a trigger that operates a solenoid. The applied magnetic force removes a poppet from the orifice of the nozzle. The opening time can be varied. Typically it is 1 ms. Through a conical shaped supersonic nozzle the gas then expands into vacuum. 3.4 Diagnostics The quantitative measure of the neutron yield requires detectors that have a time response of a few nanoseconds. Otherwise it would be impossible to distinguish between the desired 2.45 M ev fusion neutrons, scattered neutrons, x-rays and cosmics. Also a high sensitivity is needed. The detectors have to be capable of tracing 32

44 single particles. Neutron emission is observed by four scintillating neutron detectors. They are composed of a cylindrical plastic scintillator with a diameter of 12.7 cm and 15.0 cm length and a photomultiplier tube (PMT) with 12.7 cm diameter, connected by a conical Plexiglas light guide. Figure 3.4: Photo of the target chamber. The picture shows a typical setup for an experiment. Two detectors for energetic x-rays are positioned close to the chamber and a neutron detector is situated at an elevated position. The other detectors are to far away from the chamber to be seen here. The laser comes in from the right side. The fusion reactions take place in the chamber in the center of the picture. The plastic scintillator takes advantage of the fact that the cross section for neutron-hydrogen interactions is comparatively large. Whereas neutrons easily penetrate most other materials, their mean free path in hydrogen compounds is in the order of a few centimeters. Neutrons can transfer significant amounts of their 33

45 energy to recoiling protons which subsequently excite atoms (and also some molecule vibrations) in the medium. When decaying back to their ground state these atoms emit so called scintillation light. It can be assumed, that for each 620 ev of depleted proton energy one photon of nm wavelength is created in the scintillator [42]. The material is highly transparent for the scintillation light. A reflective UV coating reflects 80 % of the photons into the conical light guide that ends at the PMT. Internal reflections between scintillator, light guide and PMT are avoided by using an index matching oil for the connections. The PMT has a wide dynamic range because the number of expected neutrons varies significantly, depending on the neutron yield and the distance from the detector to the source. It has a gain of 10 7 and an impedance of 50 Ω. The signals were recorded with a 5 GHz Oscilloscope with a high bandwidth transient. A typical setup of diagnostics is shown is Fig

46 Chapter 4 Characteristics of the Cluster Neutron Source In the following we will present results that characterize the cluster neutron source in several ways. 4.1 Cluster Size Measurements The maximum ion energies highly depend on the cluster size distribution and so a good estimate of the average cluster size is important for interpreting results. One method to do this is Rayleigh Scattering [43, 44]. We have chosen this method, because it is non-destructive and the experiment is easy to perform. The Rayleigh technique can be used for cluster sizes from 100 (the limit of scattering light detection) to > 10 6 (the limit given by the scattering cross section) atoms per cluster. Optical scattering from a cluster jet typically occurs for a threshold of N C 150 atoms per cluster [45, 44]. Measuring the pressure scaling of scattering after this point allows us to estimate the average cluster size. 35

47 Figure 4.1: Measured pressure scaling of Rayleigh scattering signals for a) argon at 293 K, b) xenon at 293 K, c) methane at 293 K and d) hydrogen at 80 K. The scattering experiment was performed using a Nd:YAG laser providing a 532 nm long pulsed (a few ns) beam. The scattered light was collected by a lens with a clear aperture of 50.8 mm at 90 from the incident laser and imaged to a photo-multiplier tube. Background light was blinded out to a high degree. For spherical clusters the scattering signal S RS is proportional to n 0 N C, where n 0 is the density before clustering. We know that n 0 is proportional to the backing pressure P 0 and hence find S RS P 0 N C. The pressure scaling was measured for argon, xenon and methane at room temperature and for hydrogen for a reservoir temperature of 80 K. The results 36

48 are shown in Figure 4.2. The observed pressure scalings for argon and xenon are in general agreement with data reported in literature [41, 45, 46]. We estimated the cluster sizes for the pressures that are typically used in the various experiments in our lab. For argon at 670 psi we found an average cluster size of about atoms per cluster corresponding to a diameter of 6.7 nm, for xenon at 200 psi we estimated atoms per cluster corresponding to a diameter of 8.3 nm, for methane at 1000 psi we estimated 430 atoms per cluster corresponding to a diameter of 4.2 nm and for cooled hydrogen at 1000 psi we estimated atoms per cluster corresponding to a diameter of 2.9 nm. Figure 4.2: Measured temperature dependance of Rayleigh scattering signals for methane (left) and argon (right) In addition to the pressure scaling we also observed the temperature dependance of the average cluster size for methane and argon. The temperature scaling depends on the Hagena parameter, the cluster size, the density and the Rayleigh cross section. The scattering signal S RS is proportional to N C. For methane we find S RS T 2.4 and for argon we find S RS T 4.7. Since for both gases optical scattering can still be observed at room temperature, so that the onset of scattering cannot be identified, we can not use this scaling to determine the cluster size. 37

49 4.2 Time of Flight Histograms The detectors we used are not only sensitive to neutrons, but also to charged particles and energetic rays like x-rays which are emitted from the plasma filament. However most of those are shielded by the metal chamber walls. A method to distinguish fusion neutrons, scattered neutrons, x-rays and cosmics is to record time of flight (TOF) histograms. For every measurement such a histogram was plotted. Figure 4.3: Time of flight histogram for a neutron detector in a distance of 4.37 m from the neutron source. In Figure 4.3 one can clearly distinguish x-rays from fusion neutrons. The data were taken by a detector positioned 4.37 m away from the neutron source. Neutrons with an energy of 2.45 MeV travel with a velocity of ns m and x-rays 38

50 propagate with the speed of light. For a distance of 4.37 m this corresponds to a time of flight of ns for neutrons and 14.6 ns for x-rays. This is in good agreement with the two peaks in the time of flight data. We can see, that the source is very clean and little x-ray emission comes along with the desired neutrons. The neutron peak is followed by a tail of signals that are affected by scattered neutrons. During the scattering process these neutrons lose energy and hence velocity. In some of the histograms we found another small peak between the signals from x-rays and neutrons. This peak might correspond to more energetic 14.4 M ev neutrons with a velocity of ns m. Those neutrons typically are created in a fusion reaction of deuterium and tritium. Therefore it is possible that tritium generated by the reaction D + D T (1.01MeV ) + p(3.02mev ) undergoes a secondary fusion reaction yielding 14.4 M ev neutrons. Since the signals in the appropriate area were small we need an increased neutron yield to confirm the existence of D+T fusion processes in the plasma filament. 4.3 Pressure Dependance of the Neutron Yield To find the optimum backing pressure for cluster fusion experiments, we scanned the pressure dependence for a range of psi. The energy on target was 320 mj. Larger clusters lead to higher laser absorption [10]. According to equation 2.19 the maximum kinetic energy of the deuterons increases with the cluster radius. Hence a higher neutron yield is expected for larger clusters. Figure 4.4 shows that the yield increases as pressure rises. After passing a rollover point at 1000 psi, the yield decreases as the pressure increases. This rollover can be explained by propagation effects in the low density wings of the cluster plume. As the pressure rises the cluster diameters in the plume increase and so does absorption. At the rollover point absorption by clusters in the outer regions 39

51 Figure 4.4: Measured pressure dependance of the neutron yield for an energy on target of 320 mj. of the plume depletes the laser energy before it penetrates into the high density regions of the jet. For most of the following experiments we used a backing pressure of 1000 psi to achieve a high yield. 4.4 Energy Dependance of the Neutron Yield One great advantage of the cluster fusion neutron source is, that the neutron yield scales favorably with increasing laser pulse energy [12]. We observed the energy dependance of the neutron yield for deuterium clusters for energies of mj. For this measurement we cooled the gas in the jet to about 80 K and used a backing pressure of 1000 psi. 40

52 Figure 4.5: Measured energy dependance of the neutron yield for a backing pressure of 1000 psi and a gas jet temperature of 80 K. From Figure 4.5 we can see that the fusion neutron yield increases with higher laser energies. Using the least mean squares fit to a power law dependance, the scaling was found to be E 2.23 for low energies. This is consistent with previous results [12]. However the scaling changes at 220 mj to almost linear. This might be due to a pre-pulse of the laser beam. At high energies such a pre-pulse can have sufficient intensity to partially ionize the clusters. This would lead to an expansion before the main pulse arrives. The average kinetic energy for ions and therefore the fusion neutron yield from Coulomb explosions of pre-expanded clusters obviously is smaller. The maximum yield observed in this experiment was neutrons per shot. 41

53 4.5 Polarization Scan For the case of CD 4 clusters we measured the polar distribution of the neutron emission. The laser light provided by the THOR laser is linear polarized. Since it is the laser electric field that accelerates the electrons, this might also have an impact on the direction in which the ions get their kinetic energy. A preferred direction for ion velocity might than result in a enhanced neutron yield along the axis of polarization. Using a λ/2 waveplate we were able to scan the polarization dependance over the full range of 180. For the measurements we used a 40 fs, 50 mj pulse. The gas jet had a backing pressure of 1000 psi and was cooled down to 273 K. We measured the neutron yield at seven different polarizations with two detectors in positions shifted by 90 to each other. A third detector recorded the overall yield so that we were able to subtract the fluctuations of the total yield. For each polarization 700 shots were taken. Subsequently the signals were averaged and the obtained average peak height was interpreted as a measure for the neutron yield. The data plotted in Figure 4.6 show no obvious dependance on the polarization of the incoming beam. From this we can conclude that the cluster expansion is isotropic or at least independent of the polarization of the ionizing e-field. Furthermore the ion kinetic energy is not enhanced significantly by the laser electric field. This measurement gives no information about the distribution of the neutron yield in the polar plane for a fixed polarization of the incoming light. This distribution might show an anisotropy due to the unsymmetrical shape of the cluster plume. Such a measurement would yield information about the contribution of fusion events in the cold plume to the total neutron yield. Regrettably we could not perform this experiment because of the geometry of our target chamber. 42

54 Figure 4.6: Measured polarization dependence of the fusion neutron yield. (F. Bürsgens et al., to be published) 4.6 Angular Distribution of the Neutron Yield As discussed in chapter two the angular distribution of the neutron yield is expected to have a small anisotropy. An azimuthal scan performed by Grillon et al. [26] showed an anisotropy of the neutron yield for a source similar to the one we occupied. As clustering gas they used deuterated methane. However their results do not show the expected enhancement in forward and backward direction, but an inordinate structure. They explain this pattern with the contribution of fusion events in the cold plume to the total yield, which they suspect to be higher than discussed in the model above. Since these results were rather surprising, we performed a measurement of the angular distribution to ascertain the results. We used a setup almost identical to that employed by Grillon et al.. Deuterated methane clusters were produced with a backing pressure of 1000 psi pre-cooled to approximately 275 K by the supersonic 43

55 nozzle. This corresponds to a cluster size of 4.5 nm. A 40 fs pulse with energies of mj irradiated the target. Because of the chamber design (Fig. 3.4) variations in the attenuation of the neutron flux owing to different amounts of material (e.g. by flanges or windows) along the path of the neutrons are a major issue for an angular scan. Therefore the detector was situated at an elevated position with respect to the gas jet looking down at an angle of As can be seen from Figure 3.2 for these locations the path of the neutrons is similar for every angular position. The distance between the nozzle and the center of the scintillator was 0.28 m. In order to account for fluctuations in the overall yield two additional detectors remained at the same position during the whole measurement as normalization. The number of shots taken for a single azimuthal angle varies from 200 to Figure 4.7 shows the results of the angular scan. Due to the elevated position of the detector the generated data has a polar component in addition to the desired azimuthal component. For Figure 4.7 this already was taken into account by projecting the data points onto the plane of the laser. The variation of the statistical errors reflects the variation in the number of shots for each data point. We can clearly see an anisotropy in the plot. Forward and backward direction appear to be preferential directions of neutron emission. The observed anisotropy reveals a difference of 40 % for the forward direction compared to a direction perpendicular to the laser axis. However the observed pattern is not consistent with the pattern observed by Grillon et al.. To compare the data with the theory we simulated the expected distribution for an average ion temperature of 12 kev. The results are also given in Figure 4.7 represented by the red curve. The simulation is based on a model of cylindrically shaped plasma which is surrounded by a spherical beam target. A random spacial distribution of clusters and a Maxwellian distribution for the particle velocities were 44

56 Figure 4.7: Measured and simulated angular distribution of the neutron yield. The blue squares show the experimental data. Differences in the lengths of the error bars reflect the amount of shots taken for each position. The result of a simulation for a filament with an average ion temperature of 12 kev is given by the red curve. (F. Bürsgens et al., to be published) assumed. The results were obtained by calculating the probability for fusion events in every azimuthal direction. The simulation shows the expected increased yield along the laser axis. Compared to the backward direction the neutron emission in forward direction is slightly augmented due to the geometry of the beam target. 4.7 Conclusions In this chapter we have presented a series of measurements that characterize the cluster fusion neutron source. We have shown a method to distinguish 2.45 M ev 45

57 fusion neutrons from other energetic radiation like x-rays, scattered neutrons or cosmic radiation. We have estimated the average cluster sizes produced by the gas jet for argon, xenon, methane and hydrogen. For typical pressures and temperatures we found cluster sizes of 3 10 nm. The ideal cluster diameter for deuterium cluster fusion experiments was found to be roughly 1000 psi. Furthermore we observed on what parameters the neutron yields depend. We found that the neutron yield scales favorably with laser energy. For low energy the yield is well characterized by the power law dependence on pulse energy Y E The neutron yield seems to be isotropic in polar direction, but we observed an anisotropy for the azimuthal direction. This anisotropy is qualitative consistent with a simulation of the processes in the plasma filament. 46

58 Chapter 5 Calibration of a Neutron Detector In this chapter we present a novel method of calibrating a neutron detector designed for single shot operation. The detector was designed for operation on experiments performed on the Z facility [30, 31] at Sandia National Laboratories. The detector will observe the fusion yield on the Z-machine [47]. 5.1 The Sandia Z Accelerator The ultimate goal of the experiments performed on Z is to produce electric power via inertial fusion confinement (ICF) [21]. ICF requires that small spherical shells filled with deuterium (and often also tritium) get evenly compressed to a very high density. At Z this is achieved by a z-pinch driven hohlraum. Two z-pinches are created by a nested wire array, which consists of two concentric wire arrays. Each array is composed of wires of 1 2 cm length with a thickness of less than 10 µm [48]. A schematic picture of the geometry is shown 47

59 Figure 5.1: Schematics of the Z-machine at Sandia National Laboratories. The electric energy stored in 36 Marx generators (red) discharge through pulse forming lines (blue) into the wire arrays in the center. (R. B. Spielman et al. [31]) in Figure 5.2. The discharge of electric energy through the wires creates a magnetic field. Lorentz forces than compress the exploded wire array with a extremely high velocity. At the magnetic axis the vaporized particles collide with each other. The kinetic energies of the particles are high enough to produce significant radiation. By this radiation the surrounding walls of the hohlraum are heated. Subsequently the walls emit x-rays that drive the ICF capsule. The advantage of this method is that the indirectly driven capsule gets compressed with a high symmetry because of the uniform illumination of its surface. To achieve a substantial compression of the pellet the x-ray power has to be enormous (i.g. > 100 T W [31]). To reach this a total electric energy of 11.4 MJ is stored in 36 Marx generators providing a current of up to 20 MA through the wire arrays. Highly synchronized laser-triggered switches allow the stored energy to be discharged simultaneously. The wires in the arrays are made of Tungsten which has the highest strength to weight ratio of all materials. Tungsten plasmas are very efficient radiators at the pinch temperatures and the plasma densities found on Z. The heating and vaporizing of these wires is initiated by a current pre-pulse with a 48

60 Figure 5.2: A schematic illustration of the double z-pinch driven hohlraum. Two wire arrays form a plasma that isotropically heats the hohlraum in between. The fusion pellet is situated in the center of the hohlraum. Through the hole in the case the pellet can be illuminated by the Z-beamlet for imaging the compression. peak current of 300 ka. The main current pulse completes the vaporization and ionization process. As a result of the huge currents powerful magnetic fields arise that pinch the plasma on a vertical axis. The radiation from collisions of particles in the plasma heats the hohlraum walls to 150 ev. For the x-ray radiation emitted from the walls a power of 290 T W have been observed [48]. This results in a compression of the pellet to about half its initial radius. 49

61 5.2 The Neutron Detector on Z One of the principal diagnostics in large scale inertial confinement fusion experiments is a measurement of the absolute fusion neutron yield. For this reason a high sensitivity neutron detector was designed [29]. This detector will be used in single shot dd-pellet ignition experiments [32] in which a relatively small fusion neutron signal must be distinguished from a strong flux of bremsstrahlung radiation. With this in mind, the detector has been constructed with a unique shielding geometry. Figure 5.3: Schematic illustration of positioning of the neutron detector on Z. The detector will be situated in the shielding case on the right. (L. E. Ruggles et al., [29]) In Figure 5.3 the location of the detector on the Z experiment is shown. The detector is positioned close to the target chamber. Its shield and support structure rest on the Z transmission lines inside the Z vacuum vessel. The detector consists of a scintillator and a microchannel plate photomultiplier tube (MCPPMT). A prism coupled with index matching grease reflects light from the scintillator onto the photocathode of the MCPPMT. With a thickness of 50

62 75 mm the scintillator (Saint Gobain type BC420) matches the dd-neutron mean free path of 75 mm. Its 100 mm 25 mm front surface area is located 90 cm from the ICF capsule. The scintillator is coated with T io 2. Along with the power supply and a diode laser alignment system the whole array is sealed in an air-filled aluminum housing. The detector geometry is shown in Figure 5.4. Figure 5.4: Schematics of the detector design. The upper picture shows the shielding geometry and the lower picture sketches the detector design. The MCPPMT (Burle ) has a response time of 2 nanoseconds. Combined with the neutron transit time and the 1.3 nanosecond response of the scintillator it produces a 3 to 5 nanosecond single neutron response [29]. The effects of this fast system response are ability to differentiate between prompt neutron signals from scattered neutrons and a high signal to noise ratio. Z produces abounding amounts of high photon energy x-rays. Since both 51

63 the scintillator and the MCPPMT are sensitive to x-rays the detector requires a shielding against bremsstrahlung. The scintillator response to high energy x-ray photons and 2.45 MeV fusion neutrons is roughly the same, but the number of high energy x-rays is about eight orders of magnitude greater than the expected number of neutrons. Hence the shielding has to fulfill very special requirements. Up to 54 cm of steel and 31 cm of tungsten are situated between the scintillator and the capsule area. The geometry of the double z-pinch (Fig. 5.2) allows an almost unimpaired neutron flight pass and severely attenuation of x-rays at the same time. Furthermore the MCPPMT is placed to one side of the scintillator to avoid exposure to x-rays from the pinch area. The shielding geometry is shown in Figure??. It provides adequate attenuation of x-rays up to 4 MeV. 5.3 Calibration Data The Z accelerator at Sandia National Laboratories is a single shot machine. This limited repetition rate requires the use of a neutron detector which is well calibrated to measure the absolute yield on a single shot. The calibration was performed by driving the cluster fusion source the laser system providing 40 fs pulses at a wavelength of 800 nm and a repetition rate of 10 Hz. The laser pulse with energy of J was focused into a dense plume of deuterium clusters by an f/10 spherical mirror to an intensity of W/cm 2. Clusters were generated using a gas jet consisting of a 24 mm long conical nozzle with an opening angle of 10 and an orifice of d = 750 µm. The deuterium gas reservoir backing the jet was cryogenically pre-cooled to 100 K with liquid nitrogen and expanded from a pressure of 70 bar into vacuum to form clusters of radius approximately 3 10 nm (with a rather broad size distribution). The clusters were irradiated approximately 2 3 mm under the nozzle where the average atomic 52

64 density was cm 3. In principle, neutrons can be produced at the 10 Hz repetition rate of the laser. However, in this experiment, the gas jet was operated once every six seconds because of the limited pumping capability of the vacuum system. Figure 5.5: Schematics of the setup for the calibration. The calibrated detector is marked with a D. The neutron detector is operated far below its saturation level, and hence the signal produced in the scintillator is proportional to the total neutron yield. The bias voltages of the photomultiplier tube were varied from 2800 V to 3500 V to observe the effects on the signal. During the calibration the detector was positioned at a distance of 2.0 m from the laser focal spot. This distance assured that, with an appropriately lowered fusion yield, neutrons were observed in single particle detection mode with roughly one neutron observed every 10 shots. The signal was recorded with a 5 GHz oscilloscope and the small initial x-ray pulse was easily distinguished from the much larger neutron pulse which arrived 100 ns later. The total neutron yield was also monitored with four additional neutron detectors 53

65 placed at distances of 0.40 m, 2.21 m, 2.40 m and 6.10 m. The schematic of the calibration is illustrated in Figure 5.5. To discern the dd-neutrons we plotted a time of flight histogram of the measured data. A representative TOF spectrum from the Z neutron detector is illustrated in Figure 5.6. This shows the separation between x-rays and fusion neutrons. The zero time point was determined from the arrival of the initial x-ray pulse. We identify the peak in the histogram at 92.8 ± 3.7 ns as the 2.45 MeV neutrons from the dd-fusion reaction. This time of arrival is consistent with the expected time of flight of 92.38ns for a 2.00 m distance. The low-energy tail of the neutron peak is due to scattered neutrons from the surrounding walls of the lab. The small peaks before 20 ns are caused by ballistic x-rays from the plasma and scattered x-rays from the chamber walls. Figure 5.6: Measured time of flight data. All signals over the noise level of 0.55 mv are plotted in this diagram. The included graph shows a typical signal of a single shot. 54

66 A typical operating voltage for the detector will be a MCPPMT bias voltage of 2800 V. We recorded 7000 shots at this setting. A discrimination threshold was set at 0.55 mv and only peaks above this limit were taken into account. We assumed that signals occurring in a time window of 22 ns were generated by unscattered neutrons. Using this condition, a total number of 643 shots showed fusion neutrons with energy of 2.45 MeV. The number of neutrons produced in the deuterium plasma was regulated by varying the laser pulse energy so that less than every tenth laser pulse resulted in a signal on the detector. Previous experiments have shown that the fusion yield in these deuterium cluster plasmas varies roughly as the square of the laser energy [12]. With a laser energy of 0.2 J the total neutron yield was about neutrons per shot, confirmed by the detector furthest away from the target assuming an isotropic neutron distribution. This yielded a suitable neutron flux level for the calibration. At a 2.0 m distance from the fusion plasma this corresponds to < 700 neutrons during 7000 shots on an area equal to the detectors scintillator surface area assuming an isotropic neutron distribution. This is in good agreement with the number of signals recorded. For every fusion neutron signal above the threshold value and within the 22 ns TOF window, the peak areas were calculated. The signals were integrated for a time window of 60 ns to reduce the errors arising from ringing in the acquisition circuit. None of the signals showed a second peak from scattered neutrons or other rays during this time interval. Figure 5.7 shows the histogram of peak areas. Its shape results from the distribution of energy that the neutrons transfer to the scintillating material. The average peak area was found to be ± 0.87 mv ns. It is expected, that the detector will interact with 245 ± 16 neutrons [29] on Z leading to a statistical uncertainty of 8 %. With higher MCPPMT voltages the peak areas increase exponentially. Though 55

67 Figure 5.7: Measured histogram of peak areas. 643 signals during 7000 shots were assumed to be caused by unscattered neutrons. The histogram of peak areas gives information about the average signal form. the statistics in this analysis were not as good as above, the measured sensitivity on this voltage agreed with the normalized single photoelectron MCPPMT gain stated by the manufacturer. Figure 5.8 shows the average peak height as a function of MCPPMT voltage. voltage. The average pulse height appears to vary linearly with bias 5.4 Conclusions We have presented a novel method to calibrate neutron detectors designed to measure total fusion neutron yield from single shot fusion experiments. We used 56

68 Figure 5.8: Measured average pulse heights at different bias voltages M ev neutrons from the plasma created by laser irradiated deuterium clusters. We find that this cluster fusion source is an ideal neutron source for this application, as it is very monochromatic, is largely clean from x-rays and drives from a point like pulsed source with well defined flight time to the detector. The source provided neutrons at a high enough repetition rate to achieve statistics that limit the error for measurements using the detector almost completely to the statistical uncertainties of the total yield. 57

69 Chapter 6 Pulsed Magnetic Mirror Confinement of the Plasma Filament Before the cluster neutron source can be used for material science and some other applications, the neutron yield has to be increased by some orders of magnitude. The further progress on laser systems will definitely help to increase the neutron production, but the required number of neutrons can only be reached by other improvements. 6.1 Confinement of the Plasma Filament From equation 2.26 we can see that a longer disassembly time of the plasma will result in a higher yield. One possibility to achieve this is to apply a magnetic confinement device to the cigar shaped plasma filament. The possibility of combining a hot, laser produced plasma with a magnetic confinement device was first discussed 58

70 by Mayer, Berk and Forslund [49]. Since the disassembly time of the plasma is < 100 ps a significant enhancement of the neutron yield could be achieved even for confinement times in the order of a few nanoseconds. The plasma expands predominantly in radial direction. We want to confine the plasma at densities close to the initial density of cm 3. The point where the plasma pressure equals the magnetic field pressure can be found with the plasma parameter β which is given by β = 2µ 0nkT B 2 (6.1) Stagnation of the plasma is achieved at the point where β = 1. For ion densities between cm 3 and cm 3 and a temperature of 5 10 kev this requires peak B-fields around 200 T. Furthermore the Larmor radii should be less than the plasma size to achieve confinement in the radial direction. The initial diameter of the plasma filament is about 100 µm. To force 10 kev deuterons on an equivalent gyro radius B-fields of more than 150 T are needed. Figure 6.1: Schematic of magnetic mirror confinement 59

71 The confinement time of the plasma is limited not only by the pulse duration of the magnetic field, but also by the particle losses through cross field diffusion of the plasma in radial direction and through the loss cone of the magnetic mirror. It turns out that for the desired two loop configuration the cone losses give the dominant time scale τ cone = 0.78τ ii ln Bmax B min 1 (6.2) This longitudinal escape time depends on the ion-ion collision time τ ii and the ratio of the maximum magnetic field B max to the minimum magnetic field B min. For ion densities of cm 3 the plasma confinement time is 100 ns. Hence a magnetic field of more 200 T for 100 ns should be able to increase the fusion yield by a factor of 1000 over previously observed yields in this experiment. Figure 6.2: Schematic illustration of the circuit design for pulsed magnetic confinement. 60

72 Figure 6.3: Schematics of laser triggered spark gap. The gap between the electrodes is closed by a laser induced plasma. 6.2 Creating a High Magnetic Field As we have discussed above for a reasonable confinement time the peak magnetic fields required for substantial yield enhancement have to be > 200 T. Our approach to this problem uses a small, pulsed magnetic magnetic mirror configuration consisting of two coils. 61