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Novel Avenues of Wakefield Acceleration: Fusion Plasmas and Cancer Therapy

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Novel Avenues of Wakefield Acceleration: Fusion Plasmas and Cancer Therapy UC Irvine UC Irvine Electronic Theses and Dissertations Title Novel Avenues of Wakefield Acceleration: Fusion Plasmas and Cancer Therapy Permalink https://escholarship.org/uc/item/0v88226r Author Nicks, Bradley Scott Publication Date 2019 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA, IRVINE Novel Avenues of Wakefield Acceleration: Fusion Plasmas and Cancer Therapy DISSERTATION submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in Physics by Bradley Scott Nicks Jr. Dissertation Committee: Professor Zhihong Lin, Chair Professor Toshiki Tajima Professor Roger McWilliams 2020 © 2020 Bradley Scott Nicks Jr. DEDICATION To Amanda Johnson, my constant anchor on sanity. This achievement is as much your doing as mine. ii TABLE OF CONTENTS Page LIST OF FIGURES v ACKNOWLEDGMENTS ix CURRICULUM VITAE x ABSTRACT OF THE DISSERTATION xii 1 Introduction 1 1.1 Particle Trapping and Wakefield Acceleration . 1 1.2 Ion-Cyclotron Waves in a Field-Reversed Configuration . 5 1.3 Outline for Subsequent Sections . 8 2 Modeling Kinetic IC Modes in the SOL Environment 9 2.1 Analytical Modeling of IC Modes . 9 2.2 PIC Simulation of the SOL . 17 3 Beam-Driven IC Modes in the SOL of an FRC 21 3.1 IC Waves Propagating Parallel to the Magnetic Field . 22 3.2 IC Waves Propagating Obliquely to the Magnetic Field . 25 3.3 IC Waves Propagating Perpendicular to the Magnetic Field . 27 3.4 Analogy to a Proton-Boron-11 Plasma . 31 3.5 Summary and Conclusions . 33 4 Wakefield Acceleration with IC Resonance 36 4.1 Magnetized Wakefield Acceleration . 36 4.2 Cyclotron Resonance Condition . 44 4.3 Enhancement from Beam Bunching . 45 4.4 Conclusions . 48 5 High-Density Laser Wakefield Application to Oncology 50 5.1 Introduction . 50 5.2 Acceleration in the High-Density Regime . 53 5.3 Laser Intensity Scaling . 61 5.4 High-Density LWFA in Fiber Lasers . 64 iii 5.5 Electron Tissue Penetration . 70 5.6 Conclusions . 71 6 Conclusions 75 6.1 Wakefield Acceleration with Ion-Cyclotron Waves . 75 6.2 High-Density Laser-Wakefield Application to Oncology . 77 Bibliography 79 A Perpendicular Integrals of the Beam Velocity Distribution 86 A.1 Summation Forms . 86 A.2 Selected Analytical Properties . 89 A.2.1 Beam Perpendicular Integral Functions . 89 A.2.2 Maxwellian Perpendicular Integral Functions . 90 B Plasma Reactivity Calculation 92 B.1 Primary Method . 94 B.1.1 Correlation . 94 B.1.2 Variable Transform 1 . 94 B.1.3 Convolution . 95 B.1.4 Variable Transform 2 . 95 B.1.5 Final Result . 95 B.2 Alternative Method . 96 iv LIST OF FIGURES Page 1.1 A schematic representation of the C-2U plasma, with red representing the core, where plasma density is highest. The magnetic field is indicated by the black lines with arrows denoting field direction. The red arrow indicated the FRC rotation. 7 2.1 A sample dispersion relation from the supplemental approach of numerically solv- ing Eq. 2.1 for the given plasma parameters for a deuterium plasma and hydrogen beam. In this particular case, k = b = 0 and nb_ni = 0:01. The red points indicate growth (instability), and the blue points indicate damped modes. Black indicates marginal stability. The solid lines indicate the Alfvén speed, and the dashed line indicates the beam resonance lines. 17 2.2 A schematic representation of the 1D PIC simulation geometry. The one degree ⃗ of spatial freedom is taken as the ̂x direction, with the external magnetic field B0 oriented in the x-z plane at an angle k with respect to ̂x to define the angle of wave propagation. The beam population is given perpendicular and parallel components ⃗ with respect to B0 according to the angle b...................... 19 3.1 Dispersion relations for right-handed (3.1a) and left-handed (3.1b) components of ◦ the electric field for purely parallel propagation .k = 0 / and no beam population. Frequency is normalized with respect to the background ion (deuterium) cyclotron frequency Ωi, and the wavevector is normalized with respect to vA∕Ωi. The space where ! < 0 indicates backwards propagation. The intensity at at particular mode is indicated by the heat-map and is normalized with respect to the maximum value. The Alfvén velocity ! = kvA is indicated as a dashed line. The dotted line indicates the approximate region of strong ion cyclotron damping, ! = 2kvti ,Ωi. 23 3.2 The dispersion relation for right-handed (3.2a) and left-handed (3.2b) components ◦ of the electric field for purely parallel propagation .k = 0 / and a purely parallel- ◦ streaming beam population .b = 0 /. The right- and left-handed beam resonance lines .! = k∥vb∥ ,Ωb/ are indicated with dotted lines. 24 3.3 The dispersion relation for right-handed (3.3a) and left-handed (3.3b) components ◦ of the electric field for purely parallel propagation .k = 0 / and nearly perpendic- ◦ ularly injected beam population .b = 75 /. ..................... 25 3.4 The dispersion relation for the compressional (3.4a) and shear (3.4b) components ◦ of the magnetic field for oblique propagation .k = 60 / and no beam population. 27 v 3.5 The dispersion relation for the compressional (3.4a) and shear (3.4b) components ◦ of the magnetic field for oblique propagation .k = 60 / and a beam population ◦ injected at b = 15 . The beam resonance lines (now with all harmonics available) are indicated by the dotted lines. 28 3.6 The dispersion relation for the longitudinal (electrostatic) component for near-perpendicular ◦ propagation .k = 85 / without a beam population. The linearly polarized shear Alfvén mode .! = k∥vA/, which has phase velocity vA cos k, is indicated by the dash-dot line. 29 3.7 The dispersion relations for the electrostatic component for near-perpendicular prop- ◦ ◦ agation .k = 85 / and a beam population injected at b = 0 . 30 3.8 The dispersion relations for the electrostatic component for near-perpendicular prop- ◦ ◦ agation .k = 85 / and a beam population injected at b = 75 . 31 3.9 The dispersion relation for the longitudinal (electrostatic) component for a boron-11 ◦ plasma for oblique propagation .k = 75 / with a proton beam population injected ◦ at b = 60 . In this particular case, k < 0 is used to indicate backwards propagation. The beam velocity is indicated by the dotted line with spacing to show comparison with the other characteristic velocities. 33 4.1 The maximum fusion enhancement P _Pth for a scan over angular parameters k (vertical axis) and b (horizontal axis). Each angular parameter is sampled in mostly ◦ ◦ ◦ 15 increments but also includes 5 and 85 . The bright peak in the upper right ◦ ◦ corner corresponds to k = 85 and b = 75 , which was used in generating figure 3.8. 37 4.2 A snapshot of the the phase space (heatmap) of ions (D) near peak mode activity overlaid with the electrostatic field (teal) normalized to the Tajima-Dawson satu- ration Es.n/ (Eq. 4.1) for n = 2. The wavelength = 2vA∕2Ωi likewise cor- responds to the n = 2 resonance of Ωi with vA. Brighter heatmap colors indicate higher phase space density. The positive x direction is to the right. 40 4.3 The phase evolution of a single tracer deuteron from t = 0 to t = 12i with the wave phase velocity .vph = vA/ indicated. The kick to a higher velocity occurs around t = 8i. ........................................ 41 4.4 The vx velocity distribution for the combined background ion and beam ion pop- ulations for the initial and final simulation timesteps for the ion-Bernstein mode shown in Fig. 4.2 with the mode phase velocity indicated. 42 4.5 The normalized ion (D) energy spectrum for various time snapshots, where i is the ion cyclotron period, and Eb is the beam (H) injection energy. At t = 0 (blue curve), all ions are thermal. 43 4.6 A sample schematic velocity distribution at initial (blue) and later (red) stages of quasilinear saturation. 44 4.7 Enhanced fusion reactivity comparison. (a) The simulated evolution of the D-D fusion power (neutron branch) normalized to the initial thermonuclear value Pth. (b) Experimental fusion enhancement in C-2U normalized to the thermonuclear value Pth. ....................................... 45 vi 4.8 The maximum D-D fusion rate normalized to the initial thermonuclear rate for ◦ ◦ various beam velocities for the case k = 85 and b = 75 . Black points have no beam bunching; red points, bunching at b = vA∕Ωi, corresponding to the resonance at ! = 2Ωi; and blue points, bunching at b = 2vA∕Ωi, corresponding to ! = Ωi. The purple point is the approximate position of the observed fusion enhancement in the C-2U experiment. 47 ◦ 4.9 A snapshot of the the phase space of ions (B) near peak mode activity for k = 75 ◦ and b = 60 overlaid with the electrostatic field with the Tajima-Dawson satura- tion Es.n/, Eq. 4.1, indicated for n = 1 and n = 2. The wavelength = 2vA∕2Ωi likewise corresponds to ! = 2Ωi, approximately the center of the continuum dis- tribution. 48 5.1 Scaling of the normalized maximum electron energy with density nc_ne for the laser intensity a0 = 1, compared with the theoretical expression for the energy gain of electrons ΔE inLWFA................................. 57 5.2 A snapshot of the electron phase space px vs. x (heat-map, with warmer colors representing higher density) and longitudinal Ex (green) and laser Ey (translucent blue) fields for the somewhat typical wakefield case of nc_ne = 10 (“blue”) and a0 = 1 after the electron acceleration has saturated. The plasma wavelength is given by p = 2c_!p. The forward edge of the laser pulse is at x_p = 16. 58 5.3 Electron phase space and field structure of the high-density (“black”) case nc_ne = 1 with laser intensity a0 = 1 at early (5.3a) and later (5.3b) stages.
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