# Presentation: 209370

## L’OASIS Program: Theory Effort

- Carl Schroeder, Brad Shadwick, Gwenael Fubiani
- Jeroen Van Tilborg, Cameron Geddes
- Wim Leemans
*LOASIS Group, Center for Beam Physics *
**Lawrence Berkeley National Laboratory**

*DoE Review, Feb 2004*

**L’OASIS Program: Theory Effort**

## Outline

-  Fluid modeling of laser wakefield accelerators (LWFAs)
-  PIC vs Fluid benchmarking
-  Pulse evolution and pump depletion
-  Improvements to fluid code (high-order methods, envelope models)
-  Warm Fluid Model
-  Two-pulse laser injection method [G. Fubiani et al., PRE, submitted (2003)]
-  Particle tracking and PIC simulations
-  Space charge blow-up of e-bunches in vacuum
-  Envelope, shell, point-to-point models
-  Ionization effects in e-beam driven plasma wakefield accelerators
-  E164 experiments at SLAC
-  Transition radiation at plasma-vacuum boundary
-  Bunch length diagnostic

## LWFA in Channel: PIC (top) vs Fluid (bottom)

- Nonlinearity increases w/ distance
- Due to radial density  variation
- Peak density in fluid code larger
- Consistent w/ finite PIC temperature
- Presence of noise in PIC
- Line Outs (E-field and density)

- OOPIC: D.L. Bruhwiler, J.R. Cary et al. (Tech-X, U. CO)
- Fluid: B.A. Shadwick et al. (LBNL)
-                                               Bull. APS 48, No. 7 (2003)

- density

- E-field

- Electron density (a0 = 1, 30 fs laser pulse)

- Axial position

- SciDAC Accelerator Modeling Collaboration

- Axial position (normalized)

- Transverse position

## Long-time evolution: Laser pulse depletion

- Physics
-  Laser pulse distortion
-  Pump energy depletion

- Full fluid model, 1D
-  Standard LWFA regime
* **a*0 = 0.5, *k*0/kp = 15, kp L =2
-  Propagation length
-        z kp =2000 (4 mm)

- Initial

- Final

- Laser Field

- Density

- Laser Field

- Axial Position

- Pulse energy vs propagation distance

*a*0 = 0.5

- B.A. Shadwick *et al*., Bull. APS 48, 7 (2003)

## Long-time evolution: Laser pulse depletion

- Full fluid model, 1D
* **k*0/kp = 15, kp L =2, *a*0 = 0.5, 1.0, 1.5
-  Propagation length
-        z kp =2000 (4 mm)

- Physics
-  More pulse distortion with increasing *a*0
-  Pump depletion does not follow “conventional” scaling laws

- Final

*a*0 = 1.0

- Final

*a*0 = 1.5

- Laser Field

- Laser Field

- Density

- Density

*a*0 = 1.5

*a*0 = 1.0

*a*0 = 0.5

- Pulse energy vs propagation distance

- Axial Position

- Propagation Distance

- Axial Position

## Fluid Code: Higher-Order Methods

- Full fluid model, 1D
-  Standard LWFA regime
* **a*0 = 1, *k*0/kp = 10, kp L =2
-  Propagation length
-        z kp =1250 (1.6 mm)

- Higher-order methods
-  All previous laser-plasma codes 2nd order
-  Higher-order differencing schemes
-  Few grid points, larger time steps, larger stability basin
-  Up to 6th order implemented
-  Up to 100 times faster

- Convergence studies:

- 2nd order

- 4th order

- Grid pts

- E-field

- Axial position

- B.A. Shadwick *et al*., Bull. APS 48, 7 (2003)

## Full Fluid vs. Envelope Models

- Full fluid model, 1D
-  Standard LWFA regime
* **a*0 = 1, *k*0/kp = 10, kp L =2
-  Propagation length
-        z kp =500 (0.6 mm)

- Envelope model
-  Quasi-static approximation
* *Time averaged
-  >1000 faster

- Laser Field

- Density

- Wake E-field

- Axial Position

- Envelope code

- Full fluid code

- Laser pulse spectrum

- Frequency

- B.A. Shadwick *et al*., Bull. APS 48, 7 (2003)

## Warm Fluid Model (Low Temperature Kinetic Theory)

- Asymptotic solution of Vlasov-Maxwell
-  Valid for small momentum spread *p* >> *mc*
-  Average momentum fully relativistic
-  No formal closure assumption
-  To lowest order in momentum spread, no assumptions about the distribution function
- Anisotropic pressure and distribution

- Example
-  Quasi-static plasma, thermal forces small   enough to not affect wake
* **a*0 = 1.5, *k*0/kp = 10, kp L =2
-  Initially 10 eV thermal plasma

- Effective temperature (width of distribution)

- Wake

- Effective Temperature

- Axial

- Transverse

- Cross-correlation

- eV

- B.A. Shadwick *et al*., PRL (in preparation)

## Colliding pulse injector: two-pulse scheme

*Simulations predict:*
-  Femtosecond bunches (L< plasma wavelength)
-  Few % energy spread
-  1-10 pC/bunch
-  40 MeV in 1 mm
-  Emittance < 1 micron

- G.Fubiani *et al*., PRE, submitted 2003

- 30 deg

- pump pulse

- colliding pulse

- Two-pulse CPI:  Colliding pulse beats with the back of pump pulse
-  Advantage:  easier to realize experimentally
-  Disadvantages: higher trapping threshold,
-                             less control of bunch quality

## Colliding pulse injection: collinear two-pulse

## Propagation of short, dense e-bunches in vacuum 

- Propagation of short, dense e-bunches in vacuum

- 3-D relativistic point-to-point-interaction code
-  Calculates space charge force on one macroparticle from all others

- G.Fubiani *et al*., in preparation

- SciDAC Accelerator Modeling Collaboration (Ji Qiang)

## Space-charge blow-up: Self-acceleration

- Longitudinal momentum gain of electrons up to *5.3 times* its initial value

- Transverse *rms* momentum increase by 30%

- Longitudinal *rms* momentum increase by a factor ~ 6.5

_*rms momentum*__ evolution as a function of time_

- _Bunch divergence @ __*ct = 6.3 mm*_

- Most of initial bunch energy is transferred to *longitudinal* kinetic energy.

- zoom

- _Electron axial momentum density spectrum as a function of time  _

## Transition radiation at plasma-vacuum boundary

- Electron Density ( x10 20 cm-3)

- z (μm)

- ~700 m

*Interferometrically-measured longitudinal plasma density profile*

- n  nc

- Lp ~ (n dz/dn) Lf ~ formation length

- n = 0

- for

-  Plasma-vacuum edge equivalent to metal foil
-  Model interface as a step transition

- e-beam

- laser

-  Coherent Transition Radiation (THz: 100 m -- 1 mm)
-  Generated at plasma-vacuum interface
-  e-bunch diagnostic

-  metallic

- T-rays

- plasma

- W.P. Leemans *et al*., PRL 91, 074802 (2003)
- C.B. Shcroeder *et al*., PRE 69, 016501 (2004)
- J. van Tilborg *et al*., Lasers Particle Beams (submitted)

## Radiation spectrum: bunch length diagnostic  

- uT= 20

- uT= 10

- uT= 5

-  [m]

-  < 100 mrad, z =15 m,  = 100 m

- For 2  /u < , spectrum strongly modified by diffraction radiation (D <<1).

- For  < 2 z , radiation no longer coherent (F <<1).

- Radiation spectrum: bunch length diagnostic

- assumed Gaussian electron beam longitudinal distribution

- Coherent transition radiation spectrum

- z= bunch length

- Bunch length obtained from short wavelength cutoff of spectrum

## Spectrum and bunch length

*Total THz energy radiated in bandwidth: *
-  = 100 m - 1 mm
- and
-  = 10 m - 1 mm

-  [m]

- z = 15 m  = 100 m

- uT= 20

- uT= 10

- uT= 5

- consistent with 15 micron (RMS) bunch length

- Preliminary L’OASIS experimental measurements:

## Plasma Afterburner: e-beam driver & Li gas Idealized Case vs. Tunneling Ionization

- Experimental approach: only 10% of Li pre-ionized
- Self-fields of intense e-beam ionizes the remaining Li  wake disruption
- For fully neutral Li, good wake with self-ionization, with a shorter e- beam

- D.L. Bruhwiler et al. Phys. Plasmas **10. **2022 (2003)

- idealized wake in 100% pre-ionized plasma

- 10% pre-ionized; 90% neutral Li; wake disrupted

- 100% neutral Li;  e- drive beam is 2x shorter

- OOPIC Code, Tech-X Corp

- SciDAC Accelerator Modeling Collaboration

-  E-157,162,164 at SLAC
-  30-50 GeV, 3 nC, z=30-600 m
-   meter-long plasma, 1014-1016 cm-3

## Positron wakes in neutral Cs (with TI) are very similar to idealized case: no need to pre-ionize the plasma

- Ez surface plot (Cs with TI)
- Ez lineout  (Cs with TI)

- Ez surface (preionized plasma)
- Ez lineout (preionized plasma)

- SciDAC Accelerator Modeling Collaboration

## Summary

-  Close connection between theory, computation, and experiment
-  Model, design, and interpret l’OASIS experiments
-  SciDAC Collaboration
-  Fluid modeling of laser wakefield accelerators (LWFAs)
-  PIC vs Fluid benchmarking
-  Pulse evolution and pump depletion
-  High-order methods, envelope models, warm fluid model
-  Two-pulse laser injection method [G. Fubiani et al., PRE, submitted (2003)]
-  Particle tracking and PIC simulations
-  Space charge blow-up of e-bunches in vacuum
-  Envelope, shell, point-to-point models
-  Ionization effects in e-beam driven plasma wakefield accelerators
-  E164 experiments at SLAC, no need to pre-ionize plasma
-  Transition radiation at plasma-vacuum boundary
-  Bunch length diagnostic
-  Other Topics
-  Laser chirp and pulse shape effects [Schroeder et al., PRE & PP (03)]
-  Laser conditioning of e-beams [Schroeder et al., submitted]