High Brightness Electron Beams: Beam Manipulation and Acceleration Using Dielectric-Lined Waveguides
Beam manipulation and
acceleration using dielectric-
lined waveguides
FRANÇOIS LEMERY, PHILIPPE PIOT
9/22/2024
1
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Motivation for Accelerators
9/22/2024
2
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Beam-Driven Acceleration
o
Voss-Weiland DESY 1982 – Can you transform kinetic energy from one bunch to another?
o
High-impedance medium
◦
Dielectric Lined Waveguides (DLW)
◦
Cylindrical/Slab symmetric
◦
Transmission – betatron functions/emittance
◦
Low cost
◦
Plasmas
◦
Matching
◦
Wavelength proportional to density
◦
Repetition rates limited to ~kHz
◦
Ease of beam transmission
CERN COURIER
9/22/2024
3
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Wakefields and the Transformer Ratio
o
Transformer Ratio
o
Fundamental wakefield theorem:
symmetric bunches R < 2.
o
Interested in large accelerating fields
(E+)
and
efficient energy transfers (R)
9/22/2024
4
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Constant decelerating fields lead to the largest R and E+
◦
Bane ‘85 exponential ramp, doorstep.
◦
Jiang ‘12 double triangle
◦
Bunch trains of varying charge (Tsakanov)
◦
Difficult to generate such distributions – generally require
masks + transverse to longitudinal EEX.
“Ideal” Transformer Ratio
Bane et al. slac note
Jiang et. al. PhysRevSTAB.15.011301
9/22/2024
5
A. Zholents, FEL14 (FRB02).
P. Piot, PhysRevSTAB.14.022801
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Search for Continuous/Smooth shapes
o
Smooth shapes are generally easier to produce
o
Coulomb force (space charge) naturally produces smooth shapes.
9/22/2024
6
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Sinusoidal Ramp
{Leads to 2 solutions:
When c is even, top solution
When c is odd, bottom solution
9/22/2024
7
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Quadratic Ramp
9/22/2024
8
o
Simplest known shape to generate
constant decelerating field
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Benchmarking
o
Previous descriptions of R were not
normalized to a specific charge.
o
Normalizing each proposed shape
yields interesting results:
9/22/2024
9
Linear Ramp
Ideal transformer ratios
Gaussian
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Temporal Laser Shaping
9/22/2024
10
o
Longitudinal laser-shaping
o
Generate longitudinal electron
distribution out of RF gun.
o
Large accelerating fields (e.g. S-
Band) can preserve relatively
high charge density distributions.
o
Support high-repetition rates
o
Use compressor at high-energy
to scale the distribution if
necessary.
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Laser Shaping Continued
9/22/2024
11
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
20
,
60
,
100
cm
1 nC, 140 MV/m
Simulations including
additional effects
o
Investigate effect of Dazzler bandwidth limitations
o
Image charge effect on cathode
o
Space charge washes out high-frequency ringing.
o
Additional simulations for compression of 5 nC
bunch in paper
9/22/2024
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
12
Choice of Structure
o
Cylindrical DLW
o
Largest gradients
o
Cylindrically symmetric ( round beams )
o
Beam breakup (BBU) (C. Li et. al PhysRevSTAB.17.091302)
o
Slab DLW
o
Slightly less gradient ~ (80 % cylindrical)
o
Cylindrically symmetric ( round beams )
o
Significant dipole suppression
o
A. Tremaine et al., Phys. Rev. E 56, 7204 (1997).
o
TUNABLE GAP!
9/22/2024
13
Linear ramp 1 nC with
various bunch lengths
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Flat-beams in Slab-symmetric Structures
9/22/2024
14
E field in MV/m/nC
emittance
ratio
1 um 4D emittance
o
Flat-beams reduce betatron
requirements
o
Variable aperture to tune to
specific frequency.
o
Smaller apertures with flatter
beams lead to larger
accelerating fields AND
transformer ratios!!! (Linear
ramp (right))
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
x 2
x 2
Ballistic bunching +
manipulation with DLWs
USING SELF-WAKE INTERACTION TO BUNCH BEAMS VIA DRIFTS AT LOW ENERGY
9/22/2024
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
15
Ballistic bunching with self-wake
o
Is it possible to ballistically bunch with self-wake? (remove jitter from conventional ballistic bunching)
o
Photo-Injector source capable of generating :
◦
< 10 MeV energy out of gun (L-Band(1.3GHz - 35 MV/m) vs S-Band(2.856 GHz – 140 MV/m), X…), energy spread.
◦
Emittances < 5 µm for S-Band. Ideal for fitting into smaller structures.
◦
Large charge densities capable of exciting strong self-wakes
o
Explore effects of various structures and combinations
9/22/2024
16
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Ballistic bunching with 1 THz DLW
S-Band Gun
DLW parameters (a, b,
ε
, L) =(350 µm, 363 µm, 5.7, 11 cm)
9/22/2024
17
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
1THz Continued..
Fitting into 11 cm structure OK (84
% transmission).
DLW length change impact.
Can we do better than BFF=0.2?
◦
Energy correlation in LPS
◦
Solution 1: Longer bunch
◦
Solution 2: Lower the frequency
9/22/2024
18
Solenoid #1
Solenoid #2
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
500 GHz DLW – (350 µm,
393 µm, 5.7)
o
Lower frequency (e.g. longer wavelength) traps more electrons
o
Smaller influence from initial LPS chirp for BFF
o
“Easier” to do ( e.g. larger inner radius structure, spectral content)
o
Higher mode suppression by under/over compressing the bunches.
9/22/2024
19
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
L-Band case study
o
Larger emittance
◦
Larger structures
◦
Lower frequencies
o
Lower energy
◦
Shorter bunching length for
same energy modulation
◦
More space charge effects
9/22/2024
20
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Numerical Simulations with ASTRA
•
Particle tracking code with space charge
•
Use 2+1/2 D – cylindrical symmetry.
•
100k macro particles,
•
200 long. bins, 7 rad. bins.
•
Use Green’s function “WAKE” ASTRA
module.
•
Use offline software to calculate the bunch
form factor (BFF)
9/22/2024
21
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
To High Peak Currents
•
L ~
λ
– Single peak.
•
Peak current limited by energy spread.
•
Scan various wavelengths and record peak
current.
•
For L-Band case, this corresponds to a peak
current of ~ 12 kA (7.1%).
•
Scalable for higher charge / large structures
a=650 µm
•
Limited by slice energy spread
9/22/2024
22
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Passive Compressor for
beam-driven applications
9/22/2024
23
•
Bunch larger portion of the bunch (50%)
•
Extremely scalable: higher charge
longer
bunches
larger structures.
•
Details: Red trace: immediately after structure,
blue trace 1.2 m (1.13 m bottom) downstream.
•
(a, b, e, L) = (1 mm,
1.05 mm, 5.7, 5 cm)
corresponding to
λ
0 = 1.948 mm
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Longitudinal Shaping
with DLW
Larger wavelengths (
λ
>>L)
◦
Bunch shaping
◦
Passive bunching
◦
De-chirper/Linearizer
Ramped bunch for high transformer
ratio acceleration.
◦
Here for (165 µm, 197 µm, 5.7)
◦
R = 7.3 (Theoretical max 9.3)
9/22/2024
24
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Cascaded Manipulation
https://portal.slac.stanford.edu/sites/ard_public/tfd/facilities/nlcta/Pages/Echo-enabled-Harmonic-Generation.aspx
9/22/2024
25
•
Can this be done at low energy?
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
EEHG with DLWs
9/22/2024
26
Before (red)
and after
(blue) DLW #1
Overbunched LPS before DLW #2
Second energy modulation from DLW #2
After subsequent drift, EEHG occurs
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Merging concepts for Acceleration
o
DLWs in series, bunch and accelerate
o
DLW dimensions limited by beam
o
Total energy gain limited by transformer ratio
9/22/2024
27
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Compact X-Ray source
o
S-band test case:
◦
E+ = ~ 111 MV/m
◦
E- = ~ 43 MV/m
◦
R = ~ 2.6
o
Dynamic processes at large gradients
o
Will require full PIC simulations
o
Look at emittance growth
9/22/2024
28
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
9/22/2024
29
Coherent THz extraction
•
Cherenkov radiator
–
Using second DLW to extract DLWs of same (or higher
harmonic) frequency.
•
Efficiency enhancement over CTR?
–
CTR scales with energy/BFF
–
Fields in DLW scale with
•
BFF/charge
•
Structure parameters
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Gracias!
Philippe Piot – Adviser from NIU/Fermilab who made this work possible, and fun.
Daniel Mihalcea—Useful discussions and simulation help.
Jun Zhu—Useful discussions and help with flat-beams.
Peter Stoltz & Tech-X for Vorpal (VSIM) help.
9/22/2024
30
HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
This presentation discusses the manipulation and acceleration of electron beams through the use of dielectric-lined waveguides. It delves into motivations for accelerators, beam-driven acceleration, wakefields, transformer ratio, and the search for continuous smooth shapes in beam technologies. Various concepts and developments in the field of accelerator physics are explored, highlighting the advancements in generating high-energy beams for scientific research and discovery.
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Presentation Transcript
Beam manipulation and acceleration using dielectric- lined waveguides FRAN OIS LEMERY, PHILIPPE PIOT 1 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
? Motivation for Accelerators oCockroft+Walton 1930-split the atom oColliders led to standard model (and beyond?) Higgs found hiding @125 GeV/c2 LHC Run #1 2012 New physics in Run2 Pentaquark (2.1 ? LHCb) 2 TeV bump (3.4 ? ATLAS & CMS) IceCube 1.7 PeV neutrinos from northern sky (PhysRevLett.115.081102) OMG particle e.g. ultra-high-energy cosmic rays E> 10^20 eV BSM searches (DM, DE, extra dimensions, SUSY?) require high energies oLight sources for other scientific frontiers SASE-based e.g. FLASH, LCLS, XFEL revolutionizing our understanding of biophysics Chemical and drug development advancements Possible future coherent gamma-ray sources for nuclear physics (need more energy!) oLimitations Cost ($13+ BN for LHC, $1 BN LCLS) Magnet strength in circular machines Acceleration gradients and length in linear accelerators (LINACs) < 100 MV/m 2 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Beam-Driven Acceleration oVoss-Weiland DESY 1982 Can you transform kinetic energy from one bunch to another? oHigh-impedance medium Dielectric Lined Waveguides (DLW) Cylindrical/Slab symmetric Transmission betatron functions/emittance Low cost Plasmas Matching Wavelength proportional to density Repetition rates limited to ~kHz Ease of beam transmission CERN COURIER 3 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Wakefields and the Transformer Ratio oTransformer Ratio oFundamental wakefield theorem: symmetric bunches R < 2. oInterested in large accelerating fields (E+) and efficient energy transfers (R) 4 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Ideal Transformer Ratio Constant decelerating fields lead to the largest R and E+ Bane 85 exponential ramp, doorstep. Jiang 12 double triangle Bunch trains of varying charge (Tsakanov) Difficult to generate such distributions generally require masks + transverse to longitudinal EEX. Bane et al. slac note Jiang et. al. PhysRevSTAB.15.011301 A. Zholents, FEL14 (FRB02). P. Piot, PhysRevSTAB.14.022801 5 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Search for Continuous/Smooth shapes oSmooth shapes are generally easier to produce oCoulomb force (space charge) naturally produces smooth shapes. 6 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Sinusoidal Ramp { Leads to 2 solutions: When c is even, top solution When c is odd, bottom solution 7 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Quadratic Ramp o Simplest known shape to generate constant decelerating field 8 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Benchmarking oPrevious descriptions of R were not normalized to a specific charge. oNormalizing each proposed shape yields interesting results: Gaussian 1 ? 9 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Temporal Laser Shaping o Longitudinal laser-shaping o Generate longitudinal electron distribution out of RF gun. o Large accelerating fields (e.g. S- Band) can preserve relatively high charge density distributions. o Support high-repetition rates o Use compressor at high-energy to scale the distribution if necessary. 10 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
20, 60, 100 cm 1 nC, 140 MV/m Laser Shaping Continued oQuadratic ramp relatively simple to generate using a polynomial laser shape (e.g. ???) see evolution (right) oTunable parameters Laser (length, shape, spotsize) Charge Acceleration gradient 11 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Simulations including additional effects oInvestigate effect of Dazzler bandwidth limitations oImage charge effect on cathode oSpace charge washes out high-frequency ringing. oAdditional simulations for compression of 5 nC bunch in paper 12 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Choice of Structure oCylindrical DLW oLargest gradients oCylindrically symmetric ( round beams ) oBeam breakup (BBU) (C. Li et. al PhysRevSTAB.17.091302) oSlab DLW oSlightly less gradient ~ (80 % cylindrical) oCylindrically symmetric ( round beams ) oSignificant dipole suppression oA. Tremaine et al., Phys. Rev. E 56, 7204 (1997). oTUNABLE GAP! Linear ramp 1 nC with various bunch lengths 13 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Flat-beams in Slab-symmetric Structures o Flat-beams reduce betatron requirements o Variable aperture to tune to specific frequency. o Smaller apertures with flatter beams lead to larger accelerating fields AND transformer ratios!!! (Linear ramp (right)) E field in MV/m/nC x 2 x 2 1 um 4D emittance 14 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Ballistic bunching + manipulation with DLWs USING SELF-WAKE INTERACTION TO BUNCH BEAMS VIA DRIFTS AT LOW ENERGY 15 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Ballistic bunching with self-wake oIs it possible to ballistically bunch with self-wake? (remove jitter from conventional ballistic bunching) oPhoto-Injector source capable of generating : < 10 MeV energy out of gun (L-Band(1.3GHz - 35 MV/m) vs S-Band(2.856 GHz 140 MV/m), X ), energy spread. Emittances < 5 m for S-Band. Ideal for fitting into smaller structures. Large charge densities capable of exciting strong self-wakes oExplore effects of various structures and combinations 16 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Ballistic bunching with 1 THz DLW S-Band Gun DLW parameters (a, b, , L) =(350 m, 363 m, 5.7, 11 cm) 17 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Solenoid #2 Solenoid #1 1THz Continued.. Fitting into 11 cm structure OK (84 % transmission). DLW length change impact. Can we do better than BFF=0.2? Energy correlation in LPS Solution 1: Longer bunch Solution 2: Lower the frequency 18 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
500 GHz DLW (350 m, 393 m, 5.7) oLower frequency (e.g. longer wavelength) traps more electrons oSmaller influence from initial LPS chirp for BFF o Easier to do ( e.g. larger inner radius structure, spectral content) oHigher mode suppression by under/over compressing the bunches. 19 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
L-Band case study oLarger emittance Larger structures Lower frequencies oLower energy Shorter bunching length for same energy modulation More space charge effects 20 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Numerical Simulations with ASTRA Particle tracking code with space charge Use 2+1/2 D cylindrical symmetry. 100k macro particles, 200 long. bins, 7 rad. bins. Use Green s function WAKE ASTRA module. Use offline software to calculate the bunch form factor (BFF) 21 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
To High Peak Currents L ~ Single peak. Peak current limited by energy spread. Scan various wavelengths and record peak current. For L-Band case, this corresponds to a peak current of ~ 12 kA (7.1%). Scalable for higher charge / large structures a=650 m Limited by slice energy spread 22 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Passive Compressor for beam-driven applications Bunch larger portion of the bunch (50%) Extremely scalable: higher charge longer bunches larger structures. Details: Red trace: immediately after structure, blue trace 1.2 m (1.13 m bottom) downstream. (a, b, e, L) = (1 mm, 1.05 mm, 5.7, 5 cm) corresponding to 0 = 1.948 mm 23 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Longitudinal Shaping with DLW Larger wavelengths ( >>L) Bunch shaping Passive bunching De-chirper/Linearizer Ramped bunch for high transformer ratio acceleration. Here for (165 m, 197 m, 5.7) R = 7.3 (Theoretical max 9.3) 24 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Cascaded Manipulation Can this be done at low energy? https://portal.slac.stanford.edu/sites/ard_public/tfd/facilities/nlcta/Pages/Echo-enabled-Harmonic-Generation.aspx 25 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
EEHG with DLWs Second energy modulation from DLW #2 After subsequent drift, EEHG occurs Before (red) and after (blue) DLW #1 Overbunched LPS before DLW #2 26 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Merging concepts for Acceleration oDLWs in series, bunch and accelerate oDLW dimensions limited by beam oTotal energy gain limited by transformer ratio 27 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Compact X-Ray source oS-band test case: E+ = ~ 111 MV/m E- = ~ 43 MV/m R = ~ 2.6 oDynamic processes at large gradients oWill require full PIC simulations oLook at emittance growth 28 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Coherent THz extraction Cherenkov radiator Using second DLW to extract DLWs of same (or higher harmonic) frequency. Efficiency enhancement over CTR? CTR scales with energy/BFF Fields in DLW scale with BFF/charge Structure parameters 29 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
Gracias! Philippe Piot Adviser from NIU/Fermilab who made this work possible, and fun. Daniel Mihalcea Useful discussions and simulation help. Jun Zhu Useful discussions and help with flat-beams. Peter Stoltz & Tech-X for Vorpal (VSIM) help. 30 9/22/2024 HIGH BRIGHTNESS ELECTRON BEAMS @ HAVANA
