Alternative approaches to rapid acceleration of ion beams

210 Pages·2014·19.7 MB·English

Alternative approaches to rapid
acceleration of ion beams − harmonic
ratcheting for fast RF acceleration and
laser driven acceleration of gas jet
targets
A Dissertation Presented
by
Nathan Michael Cook
to
The Graduate School
in Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy
in
Physics
Stony Brook University
December 2014
Copyright by
Nathan Michael Cook
2014
Stony Brook University
The Graduate School
Nathan Michael Cook
We, the dissertation committee for the above candidate for the
Doctor of Philosophy degree, hereby recommend
acceptance of this dissertation
Axel Drees - Dissertation Advisor
Professor, Department of Physics and Astronomy
Peter W. Stephens - Chairperson of Defense
Professor, Department of Physics and Astronomy
Steve Peggs - Committee Member
Professor, Department of Physics and Astronomy
Michael Zingale - Committee Member
Professor, Department of Physics and Astronomy
Brian D. Sheehy - External Member
Physicist, Brookhaven National Laboratory
Igor Pogorelsky - External Member
Physicist, Brookhaven National Laboratory
This dissertation is accepted by the Graduate School
Charles Taber
Dean of the Graduate School
ii
Abstract of the Dissertation
Alternative approaches to rapid acceleration
of ion beams − harmonic ratcheting for fast
RF acceleration and laser driven acceleration
of gas jet targets
by
Nathan Michael Cook
Doctor of Philosophy
in
Physics
Stony Brook University
2014
Energetic ion beams have vast potential in medicine, energy, and
basic science, providing significant advantages in applications of
radiation therapy, nuclear energy, and high energy physics. Con-
ventional acceleration means are inefficient and costly, imposing
stringent requirements on space, power, and speed of the ma-
chines designed to address these applications. This thesis considers
two contrasting approaches to improving ion beam acceleration:
fast acceleration using radio-frequency (RF) technology and laser
driven acceleration of ion beams from over-dense plasma.
We first consider fast acceleration in a synchrotron using conven-
tional RF cavities. We introduce a ferrite based RF scheme for
a rapid cycling synchrotron known as “harmonic ratcheting.” By
systematically decreasing the harmonic number in steps during the
acceleration cycle, a reduction in the required frequency range is
iii
achieved. Two cavities alternately provide the accelerating voltage
toallowtuning. Aratchetingapproachallowsforadoublingofgap
voltage for fixed cavity length and input power. Simulations per-
formedusinga 65msynchrotrondesign demonstrate thefeasibility
of the scheme for acceleration of C6+ ions to 400 MeV/nucleon at
a 15 Hz repetition rate.
Next, we investigate the acceleration of ions through the interac-
tion of an intense CO laser and over-dense plasma. Brookhaven
2
National Laboratory's Accelerator Test Facility possesses a TW-
class CO laser, with the unique capability to produce a single
2
intense 5 ps pulse at 10 µm. This allows for the use of high pu-
rity gas jet targets at densities which exceed the critical density
of the laser light. We demonstrate the repeatable acceleration of
ions using a two pulse technique. A pre-pulse containing a few
% of the main pulse energy arrives 25 ns prior to the main pulse,
driving a hydrodynamic blast wave into the gas target. The main
pulse then drives an electrostatic shock into the shaped plasma,
producing ion beams with higher peak energies than predicted by
other approaches. We observe accelerated beams only for a narrow
range of pre-pulse energies, indicating the importance of the target
density profile in enabling the acceleration.
iv
To my parents and to my grandparents.
Contents
List of Figures ix
List of Tables xx
Acknowledgements xxi
1 Introduction 1
1.1 High precision applications for ion beams in medicine . . . . . 4
1.2 Applications with high current and high energy . . . . . . . . 5
1.3 Motivating alternative acceleration methods . . . . . . . . . . 6
2 Periodic Accelerators 9
2.1 Transverse Dynamics . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Equations of Motion . . . . . . . . . . . . . . . . . . . 12
2.1.2 Emittance . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.3 Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.4 Lattice Design . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Longitudinal Dynamics . . . . . . . . . . . . . . . . . . . . . . 20
2.2.1 Energy gain in a synchrotron . . . . . . . . . . . . . . 22
2.2.2 Small amplitude longitudinal oscillations . . . . . . . . 23
2.2.3 Large Amplitude Oscillations and the Separatrix . . . . 25
3 Harmonic Ratcheting for Rapid Acceleration of Ions 30
3.1 Ferrite-loaded RF cavities . . . . . . . . . . . . . . . . . . . . 31
3.1.1 RF cavity basics . . . . . . . . . . . . . . . . . . . . . 31
3.1.2 Ferrites . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1.3 Ferrite-Loaded RF cavities . . . . . . . . . . . . . . . . 37
3.1.4 Cavity parameters and performance . . . . . . . . . . . 40
3.2 Harmonic ratcheting . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.1 Designing a ratcheting ramp . . . . . . . . . . . . . . . 46
3.2.2 Emittance growth at ratcheting transition . . . . . . . 46
vi
3.3 Cavity performance with harmonic ratcheting . . . . . . . . . 48
3.4 Example: a rapid cycling medical
synchrotron . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.5 Ratcheting challenges . . . . . . . . . . . . . . . . . . . . . . . 54
3.5.1 Anomalous effects . . . . . . . . . . . . . . . . . . . . . 54
3.5.2 Magnetic alloy cavities . . . . . . . . . . . . . . . . . . 55
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4 A Laser Plasma Primer 57
4.1 A plasma primer . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.1 Collisions . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.1.2 Describing plasma dynamics . . . . . . . . . . . . . . . 62
4.2 Laser-plasma interactions . . . . . . . . . . . . . . . . . . . . . 65
4.2.1 Ionization mechanisms . . . . . . . . . . . . . . . . . . 65
4.2.2 Free electron motion . . . . . . . . . . . . . . . . . . . 67
4.2.3 Propagation of waves in plasma . . . . . . . . . . . . . 72
4.2.4 Energy absorption mechanisms . . . . . . . . . . . . . 75
4.3 Ion acceleration mechanisms . . . . . . . . . . . . . . . . . . . 78
4.4 Target normal sheath acceleration . . . . . . . . . . . . . . . . 78
4.5 Radiation pressure acceleration . . . . . . . . . . . . . . . . . 80
4.6 Collisionless shock acceleration . . . . . . . . . . . . . . . . . 85
5 Experimental Configuration at BNL Accelerator Test Facility 91
5.1 ATF Terrawatt CO Laser . . . . . . . . . . . . . . . . . . . . 92
2
5.1.1 Controlled pre-pulse generation . . . . . . . . . . . . . 97
5.2 Experimental chamber and laser plasma interaction diagnostics 98
5.3 Ion beam diagnostics . . . . . . . . . . . . . . . . . . . . . . . 109
6 Diagnostic Tools for Imaging Laser Accelerated Ions 113
6.1 Film and polymer detectors . . . . . . . . . . . . . . . . . . . 115
6.2 Micro-channel plate detectors . . . . . . . . . . . . . . . . . . 117
6.3 Scintillator candidates . . . . . . . . . . . . . . . . . . . . . . 119
6.3.1 Organic scintillators . . . . . . . . . . . . . . . . . . . 119
6.3.2 Polyvinyl toluene . . . . . . . . . . . . . . . . . . . . . 120
6.3.3 Inorganic scintillators . . . . . . . . . . . . . . . . . . . 121
6.3.4 Additional properties . . . . . . . . . . . . . . . . . . . 122
6.3.5 Al O :Cr O — chromox . . . . . . . . . . . . . . . . 124
2 3 2 3
6.4 Experimental methods . . . . . . . . . . . . . . . . . . . . . . 125
6.4.1 Stony Brook tandem van de graaff . . . . . . . . . . . 125
6.4.2 CCD camera . . . . . . . . . . . . . . . . . . . . . . . 127
6.4.3 The European Machine Vision Association model . . . 127
vii
6.5 Results and analysis . . . . . . . . . . . . . . . . . . . . . . . 130
6.5.1 Yield analysis . . . . . . . . . . . . . . . . . . . . . . . 130
6.5.2 Scattering effects . . . . . . . . . . . . . . . . . . . . . 135
6.5.3 Afterglow . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7 Laser driven shock wave acceleration of ions at BNL Acceler-
ator Test Facility 141
7.1 Hydrodynamic target shaping . . . . . . . . . . . . . . . . . . 142
7.1.1 flash simulations . . . . . . . . . . . . . . . . . . . . 145
7.2 Helium ion acceleration . . . . . . . . . . . . . . . . . . . . . . 149
7.2.1 Pre-pulse regimes . . . . . . . . . . . . . . . . . . . . . 150
7.3 Particle-in-cell simulations . . . . . . . . . . . . . . . . . . . . 154
7.3.1 Shock breakdown . . . . . . . . . . . . . . . . . . . . . 160
7.4 Next steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Bibliography 172
viii
List of Figures
1.1 The corresponding dose-depth curves for various charged parti-
cles. Ions exhibit a Bragg Peak in their energy deposition near
the end of their range [1]. . . . . . . . . . . . . . . . . . . . . 3
2.1 Coordinate system in the frame of reference of a particle trav-
elling an arbitrary trajectory relative to the design path. . . . 12
2.2 Particles with the same value of action J fall on an ellipse in
phasespace. Particlepropertiessuchasmaximumdisplacement
√ √
x = 2Jβ and maximum momentum x(cid:48) = 2Jγ are
max max
described using Twiss parameters. . . . . . . . . . . . . . . . . 16
2.3 An example symmetric FODO, featuring a circular beam and
zero dispersion. . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Anentirelatticedepictedgraphicallywithparametersβ (blue),
x
β (red), and D (green) superimposed. . . . . . . . . . . . . . 20
y x
2.5 The lattice parameters β ,β , and D are plotted versus s for
x y x
the entire synchrotron. . . . . . . . . . . . . . . . . . . . . . . 21
2.6 The stability of a bunch in an RF bucket is depicted in (φ,φ(cid:48))
phase space. The stationary RF bucket (solid black line) is
accompanied by stable orbits (dashed green lines). . . . . . . . 27
2.7 The injection of a bunch into a bucket is depicted through evo-
lution in the particle phase space (φ, φ(cid:48)), where φ is the relative
phase coordinate. A “mismatched” bunch characterized by a
longbunchwithminimalmomentumvariationquicklyfilaments
and eventually fills the phase region defined by the orbit of the
particle with maximum emittance, depicted by the red line. . . 28
2.8 The accelerating bucket (solid black line) for synchronous phase
φ = π/6 along with stable orbits (green, dashed lines) is de-
s
picted in (φ, φ(cid:48)) phase space. . . . . . . . . . . . . . . . . . . . 29
ix