Diagnosis of High Energy Electron Beams Produced by Laser Wakefield Accelerators

152 Pages·2007·8.18 MB·English

Diagnosis of High Energy Electron Beams
Produced by Laser Wakefield Accelerators
by Christopher Dominic Murphy
Submitted in partial fulfilment of the requirements for the degree of Doctor of
Philosophy of the University of London and for the Diploma of Membership of the
Imperial College.
Plasma Physics Group
Imperial College
The Blackett Laboratory
London SW7 2BZ
March 2007
The copyright of this thesis rests with the author, and no quotation from it or information
derived from it may be published without prior consent of the author.
Acknowledgements
The completion of this thesis was only possible with the help and encouragement of
many people. My thanks go to them all even if space only allows me to name a few.
Firstly my supervisors: Zulf and Peter. Zulf was always there to help push along
scientific discussion with his deep knowledge of the physics and unparalleled penchant
for sarcasm. Peter was there with words of gentle encouragement whenever a confi-
dence boost was needed. Thanks also to Karl - I feel honoured to have had his help
and support.
ToStuartandAlec. IremembertheAstraexperimentswithfondness. Considering
all the late night frustrations that experimental science brings, I can only attribute
this fondness to the good company I kept.
Thanks must go to Stefan Karsch. House mate, office mate and inspiration. Few
people I have met can match his combination of scientific knowledge, hard work and
humility in abundance.
All my other fellow experimenters over the years deserve my sincere gratitide.
Christos and Malte from IC, Jordan ‘my bro’, Enrico, Richard and Dino from Strath-
clyde, Tony, Tom and Simon from Oxford. Thanks go to those who welcomed me
while abroad: All at MPQ in Garching, the IOQ in Jena, and the plasma simulation
group at UCLA - in particular Warren and Frank.
To all at RAL: Home for the past 4 years. The CLF engineers, admin staff, and
scientists alike have played their part in making my time there very happy. The Astra
group must have a special mention as without their efforts on the other side of the
shutter, this thesis would not exist. The TA group / ES group have been there to
make sure everything happened as planned. Their unique knowledge of science and
procedure was invaluable. Bob Bingham and Tito Mendon¸ca whose help brought
photon acceleration to life, and to Raoul who simulations explained it.
While all the people at the lab mean a lot to me, I must be forgiven for mentioning
some by name. Kate and James - the laughter and kindness kept me going through
it all. Peta and Rob - for providing a Sunday roast when most needed. Matt you’re
more than just Peta’s sidekick. Mags - party co-host extraordinaire. And the plasma
physics group - a wealth of plasma knowledge saving me many a trip to the library.
Now for those closest to my heart. Those who have put up with me and continue
to do so. To Lisa, my first teacher, and Andy, to Marc who makes the tough times
easy, and to my mum and dad whose continued support has made all this possible.
Thank you.
1
Abstract
This thesis discusses the production and diagnosis of electron bunches from laser
produced wakefields.
For the right laser and plasma parameters, monoenergetic features were observed
in the electron spectrum. These mononenergetic beams are found to be sensitive to
plasma density and laser parameters. In particular, the beams were found to show
shot-to-shot variations in energy and pointing. Simulations were performed to study
the mechanism of electron injection and acceleration. Further results demonstrate
how the intermittancy of the electron beam may at times be an artifact caused by
pointing instabilities.
This thesis also discusses the first reported experimental observation of photon
acceleration from a laser-produced wakefield. The spectrum of the transmitted light
from a wakefield accelerator was measured. A large density dependent blue-shifted
portion of the light was observed which cannot be explained by flash ionisation. A
photon kinetic model of the experiment demonstrates that this blue-shifting occurs at
the back of the pulse. Here, the moving density gradient of the wake provides a time-
varying refractive index suitable for photon acceleration. Thus comparison between
theory and experiment allows one to optically characterise the wakefield accelerating
structure.
Finally the thesis presents experimental measurements of the electron bunch du-
ration. A chirped probe pulse is passed through a birefringent (ZnTe) crystal close
to the wakefield generated electron bunch. Frequency components of the probe pulse
that coincide temporally with the Coulomb field of the electrons at the location of the
crystal experience a rotation of polarization due to the induced Kerr effect. Measur-
ing the spectrum of the rotated component, allows calculation of the electron bunch
duration. Limitations to the technique are discussed and the methods used to over-
come limitations are described. The results presented in this thesis constitute the
highest resolution measurement of single laser produced electron bunches thus far.
2
Contents
1 Introduction 14
1.1 Particle Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.1.1 Early accelerators . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.1.2 The Physics of Conventional Accelerators . . . . . . . . . . . . 16
1.2 Plasma Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.2.1 Advances in Plasma Accelerators . . . . . . . . . . . . . . . . 17
1.2.2 Plasma Accelerator Potential . . . . . . . . . . . . . . . . . . 18
2 Theory 19
2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.1 Plasma Parameters . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.2 Electromagnetic Definitions . . . . . . . . . . . . . . . . . . . 20
2.2 Basic Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 Plasma Frequency . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Ponderomotive Force . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 Plasma instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.1 Pulse Modulating Mechanisms . . . . . . . . . . . . . . . . . . 28
2.3.2 Resulting Instabilities . . . . . . . . . . . . . . . . . . . . . . 37
2.4 Wakefield acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.4.1 Laser Wakefield Acceleration (LWFA) . . . . . . . . . . . . . . 40
2.4.2 Plasma Beatwave Acceleration (PBWA) . . . . . . . . . . . . 41
2.4.3 Self-modulated Laser Wakefield Acceleration . . . . . . . . . . 42
2.4.4 Plasma Wakefield Acceleration (PWFA) . . . . . . . . . . . . 43
2.4.5 Dephasing and Depletion Lengths . . . . . . . . . . . . . . . . 43
3 Instrumentation 47
3.1 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1.1 Technological Overview . . . . . . . . . . . . . . . . . . . . . . 47
3
CONTENTS 4
3.1.2 The Astra Laser . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.1.3 The Atlas Laser . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2 Electron Spectrometry . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.1 Electron beam collection and preparation . . . . . . . . . . . . 54
3.2.2 Electron Dispersion . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.3 Electron Detection . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2.4 Final Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2.5 Charge measurement . . . . . . . . . . . . . . . . . . . . . . . 60
4 Electron Acceleration 61
4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.1.1 Review of Literature . . . . . . . . . . . . . . . . . . . . . . . 61
4.1.2 Controlled Self-Injection Wakefield Acceleration . . . . . . . . 63
4.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3 Experiment: Density Scan . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3.1 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 67
4.3.2 Comparison with analytic solution . . . . . . . . . . . . . . . 72
4.3.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4 Reproducibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 80
4.4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5 Photon Acceleration 84
5.1 Wakefield Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.1.1 Detection of Terahertz Radiation . . . . . . . . . . . . . . . . 85
5.1.2 Frequency Domain Interferometry (FDI) . . . . . . . . . . . . 86
5.2 The Theory of Photon Acceleration . . . . . . . . . . . . . . . . . . . 90
5.2.1 Photon Acceleration: Some Important Definitions . . . . . . . 90
5.2.2 Photon Acceleration: A Qualitative View . . . . . . . . . . . . 92
5.2.3 Mathematical description of Photon Acceleration . . . . . . . 96
5.2.4 Common examples of photon acceleration . . . . . . . . . . . 100
5.2.5 Photon Acceleration in Wakefields . . . . . . . . . . . . . . . . 102
5.3 Observation of Photon Acceleration . . . . . . . . . . . . . . . . . . . 103
5.3.1 Experimental Layout . . . . . . . . . . . . . . . . . . . . . . . 103
5.3.2 Experimental Results 1 (a = 0.8) . . . . . . . . . . . . . . . . 104
0
CONTENTS 5
5.3.3 Experimental Results 2 (a = 1.0) . . . . . . . . . . . . . . . . 107
0
5.4 Description of a Photon Kinetic Code . . . . . . . . . . . . . . . . . . 107
5.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.6 Future possibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.6.1 Future Diagnostic . . . . . . . . . . . . . . . . . . . . . . . . . 114
6 Bunch Duration Measurement 116
6.1 Electron Bunch Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.1.1 The Electric Fields Associated with Stationary Charges . . . . 116
6.1.2 The Fields Associated with Accelerated Charges . . . . . . . . 117
6.2 Optical Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.2.1 Birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.2.2 Kerr and Pockels’ Effects . . . . . . . . . . . . . . . . . . . . . 123
6.2.3 Spectro-temporal Encoding . . . . . . . . . . . . . . . . . . . 123
6.3 Experiment: Bunch Duration Measurement . . . . . . . . . . . . . . . 125
6.3.1 Experimental Set-Up: Spectro-temporal Encoding . . . . . . . 125
6.3.2 Experimental Results : Spectrotemporal Encoding . . . . . . . 128
6.3.3 Experimental Set-Up: Direct Temporal Measurement . . . . . 136
6.3.4 Experimental Results : Direct Temporal Measurement . . . . 137
7 Conclusions 140
7.1 Particle Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.2 Photon Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.3 Bunch Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
List of Figures
1.1 Lawrence’s Cyclotron [1] . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.2 The Cockcroft-Walton generator [4] . . . . . . . . . . . . . . . . . . . 15
1.3 An aerial photograph of the ‘Diamond Synchrotron’ at the Ruther-
ford Appleton Laboratory (Courtesy of CCLRC) and a schematic of a
typical large scale synchrotron (copyright (cid:13)c EPSIM 3D/JF Santarelli,
Synchrotron Soleil) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4 An aerial photograph of the Stanford Linear Accelerator. Photograph
courtesy of the U.S. Geological Survey. . . . . . . . . . . . . . . . . . 16
1.5 Acceleratorschematic: Negative(red)andpositive(lilac)chargedplates
create an electric field. The electron bunch(orange) is accelerated as
it traverses the cavity. The forces on the electrons in the cathode are
shown(green arrows). . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1 PlasmaWaveSchematic: Mobileelectrons(blackdots)oscillatearound
the immobile positive ions (grey). . . . . . . . . . . . . . . . . . . . . 22
2.2 Top: First pulse; Middle: Second pulse creating a wake π out of phase;
Bottom: Superposition of the waves results in destructive interference
of the wakes and so energy gain of the second pulse. . . . . . . . . . . 29
2.3 Photon Acceleration Schematic . . . . . . . . . . . . . . . . . . . . . 30
2.4 Laser pulse envelope (blue) in an plasma wave (red) which is at rest in
the light frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.5 The initial pulse (blue) has been modulated (black) due to variations
in group velocity in the pulse. . . . . . . . . . . . . . . . . . . . . . . 33
2.6 Thevelocityofindividualpointsalongthewavefront(blackdots)varies
withplasmadensity(redlines)andsofocusingordefocusingmayoccur
where there is any transverse variation in plasma density. . . . . . . . 35
2.7 The speed at which the spot decreases is dependant on the degree of
curvature experienced by the outermost point of the phase front. . . . 36
6
LIST OF FIGURES 7
2.8 The highest laser intensity (on axis) ionises the plasma to the greatest
extent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.9 The two waves with slightly different frequencies beat to create an
envelope modulation at a much lower frequency. . . . . . . . . . . . . 41
3.1 Laser cavity with a low Q-value (top): No photons make more than
one round trip through the active medium. Laser cavity with a high
Q-value (bottom): Closed cavity allows lasing to occur. . . . . . . . 48
3.2 The EO crystal (grey) does not allow any light to make more than
one round trip of the cavity without being rejected by the polariser
(blue). This allows a large population inversion to be built up. Once
the voltage across the crystal is crowbarred, rapid amplification of the
pulse quickly depletes the crystal and a short pulse is emitted. Image
adapted from [23]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3 (1): Modes allowed by the dimensions of the cavity; (2): Amplification
bandwidth of the lasing medium; (3) The combination of (1) and (2)
which dictates the possible output spectrum of the laser. . . . . . . . 50
3.4 A schematic of the Astra stretcher with a photograph showing what
the stretcher looks like in situ (inset). Diagram courtesy of the Astra
Group. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.5 A schematic of the Atlas laser system. The two pulses output in the
red hexagons are generated initially from the same oscillator and so
can be synchronised with relative ease and accuracy. . . . . . . . . . . 53
3.6 Regardless of the divergence of the electrons emanating from the in-
teraction point (red), a collimator tube (gray) can put an upper limit
on the divergence angle and so improve the energy resolution of the
spectrometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.7 Illustration of the v x B force. . . . . . . . . . . . . . . . . . . . . . . 56
3.8 The electron spectrometer used in this work with the electron trajec-
tory shown for a specific energy. . . . . . . . . . . . . . . . . . . . . 57
3.9 The final electron spectrometer design. The numbers are referenced in
the text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.10 The current of the moving electron bunch has an associated B-field
which in turn induced a current in the Rogowski coil. . . . . . . . . . 60
LIST OF FIGURES 8
4.1 Particle Trapping (Left): Some electron trajectories are no longer
closed loops but the wave clearly retains its coherence. Wave Breaking
(right): Too many of the electrons have ceased their oscillatory motion
and so the coherence of the plasma wave is lost. [49] . . . . . . . . . . 63
4.2 The energy of the electrons in each image increases to the right. An
energyscaleisnotdisplayedasthiswasvariedusingthemagneticfield.
The figure also shows the qualitative change in spectral shape with gas
jet backing pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3 Four single laser shots taken with the lower laser energy (a = 0.8).
0
The gas jet backing pressure was varied from 15 to 40 bar providing
fully ionised plasma densities between 3.4 and 9.1 ×1019 electrons per
cubic centimetre. This shows the electron spectra of the shots shown
in Figure 4.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4 Four single laser shots taken with the lower laser energy (a = 0.8).
0
The gas jet backing pressure was varied from 6 to 10 bar providing
fully ionised plasma densities between 1.4 and 2.2 ×1019 electrons per
cubic centimetre. This shows the electron spectra of the shots shown
in Figure 4.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.5 Three graphs showing number of electrons per percent energy spread
as a function of energy. These shots were taken with a laser normalised
vesctorpotential, a ≈ 1.1andafullyionisedplasma(electron)density
0
of2×1019 cm−3. Itisclearthatnoneofthesespectracouldbedescribed
as Maxwellian but still they vary greatly in both shape and energy. . 71
4.6 This figure graphs six single shots showing the number of electrons per
percent energy spread produced in each case against electron energy.
These are the same six shots shown in the previous two figures on one
set of axes demonstrating the extent to which the number of electrons
varies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.7 Peak energy: An analytic solution (green) and experimental data (or-
ange). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.8 Shadowgram of the plasma. . . . . . . . . . . . . . . . . . . . . . . . 73
4.9 The 16 TW (red) shot added to the 9 TW (orange) shots. The green
line is the analytical solution for the maximum energy assuming non-
relativistic dephasing over one quarter of the plasma wavelength. . . . 74
4.10 Early wakefield (left) and initial laser pulse (right) . . . . . . . . . . . 75
LIST OF FIGURES 9
4.11 Moving into the plasma, the wave amplitude increases and the laser
starts to evolve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.12 The V-shape of the plasma wavefronts is echoed by the cone shape of
the laser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.13 The curved wavefront holds much of the laser light. The light outside
diffracts quickly away. . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.14 At the end of the gas jet many electrons in many buckets are injected
and the wave loses coherency. . . . . . . . . . . . . . . . . . . . . . . 77
4.15 Injection close-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.16 Lanex detector setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.17 Electron beam pointing results . . . . . . . . . . . . . . . . . . . . . . 81
4.18 Electron beam pointing results . . . . . . . . . . . . . . . . . . . . . . 82
4.19 Light side-scattered from the wakefield at a lower density. Laser prop-
agates from left to right, field of view shown is approximately 100 x
500 microns. Images taken my M. C. Kaluza . . . . . . . . . . . . . . 83
4.20 Light side-scattered from the wakefieldas in figure 4.19 but at a higher
density. Images taken by M. C. Kaluza . . . . . . . . . . . . . . . . . 83
5.1 The ponderomotive force disturbs the charge equilibrium, setting up
localised electric transients which emit radiation in the terahertz range. 86
5.2 Thepumpcreatesplasmadensityoscillationsandthedifferenceinpath
length between the reference and probe pulses gives information about
the plasma density at a fixed position behind the driver. . . . . . . . 88
5.3 As each car passes the sign it speeds up. This increases the spatial
separation of the cars but keeps the time separation constant. . . . . 93
5.4 At one instant in time, each car slows down. The spatial separation of
the cars remains constant. The time separation will now have increased. 93
5.5 The beam (dotted arrows) impinges on a refractive index boundary
which causes the direction (and so the k vector) to change. . . . . . . 94
5.6 The beam (dotted arrows) experiences a refractive index change in
time only which causes the frequency to change but not the spatial
direction. Here, the k vector does not change. . . . . . . . . . . . . . 94
5.7 The combination of effects seen in 5.5 and 5.6 results in changes in
wavelength and frequency resulting in a more complex invariant. . . . 95