# Presentation: 565740

## Ionization Physics in Plasma Wakefield Accelerators

** ****D. Bruhwiler,****1** **D.A. Dimitrov,****1 ****J.R. Cary,****1, 2 **
**W.P. Leemans,****3 **** and E. Esarey,****3 ****C. Nieter****1**
** **

**Tech-X Corporation**
- 5621 Arapahoe Ave., Suite A
- Boulder, Colorado  80303
- http://www.txcorp.com

- 1.  Tech-X Corporation	3.  Lawrence Berkeley National Laboratory
- 2.  University of Colorado

**Work supported by US Dep’t. of Energy:**
-     DE-FG03-02ER83557  (Tech-X, SBIR)
-     DE-FG02-01ER41178  (Tech-X, SciDAC)
-     DE-FG03-95ER40926  (U. Colorado)
-     DE-AC03-76SF00098  (LBNL & use of NERSC)

## Motivation

- The “plasma afterburner” concept:
- suggests use of PWFA to double the energy of an e-/e+ collider
- S. Lee, T. Katsouleas, P. Muggli, W. Mori, C. Joshi *et al*., Phys. Rev. ST Accel. Beams **5**, 011001 (2002).
- requires two PWFA modules, driven by e- and e+ beams
- Field-induced tunneling ionization is a key effect
- The large plasma wakefields can tunnel ionize neutral gasses
- The self-fields of the drive beam can also tunnel ionize Li, Cs, etc.
- Eliminates expense & complication of preionization
- D. Bruhwiler, D.A. Dimitrov, J.R. Cary, E. Esarey, W.P. Leemans and R. Giacone, Phys. Plasmas **10** (2003), p. 2022.
- It’s necessary to simulate e+ drivers as well
- How does ideal pre-ionized case compare to tunnel-ionized case?
- How do e- driven wakes compare to e+ wakes?
- The parameters are taken from E-164x
- D. Bruhwiler, D.A. Dimitrov, J.R. Cary, E. Esarey and W.P. Leemans, Proc. Part. Accel. Conf. (2003), p. 734.

## The OOPIC Code & the IONPACK Library

- OOPIC is a 2-D (x-y & r-z) time-explicit PIC code
- developed at UC Berkeley, beginning in 1992
- J.P. Verboncoeur, A.B. Langdon and N.T. Gladd, Comp. Phys. Comm. **87** (1995), p. 199.
- Tech-X and collaborators began working with the code in 1998
- D.L. Bruhwiler, R.E. Giacone, J.R. Cary, J.P. Verboncoeur, P. Mardahl, E. Esarey, W.P. Leemans and B. Shadwick, Phys. Rev. Special Topics - Accel. & Beams, 101302 (2001).
- Available for MS Windows, Unix/Linux and also MacOS X
- http://www.txcorp.com/products/OOPIC_Pro/
- IONPACK is a C library of ionization algorithms
- Goal:  provide ionization algorithms to all community codes
- tunneling ionization (TI)
- barrier suppression ionization (BSI),
- electron-impact ionization and scattering at all energies
- supports calls from Fortran 77/90/95 and C/C++ codes
- Now being used with VORPAL (C++, 1D-3D, massively parallel)

## Parameters for 2-D (r,z) “(SLC) Afterburner” Simulations(without tunneling ionization)

- 50 GeV e- drive beam
-  r=20 m & z=63 m
- 2x1010 e- in the bunch
- r,z are normalized to e=282 m
- e- density is ne=1.4x1016 cm-3
- Grid size is z=r=7.5 m
- 34,000 beam ptcls (80 per cell)
- 56,000 plasma ptcls (7 per cell)
- Moving window is used
- Particles & fields removed at left
- Cold plasma enters at right

## Tunneling Ionization Probability Rate

- Adiabatic and quasi-classical approximations are used to calculate the probability rate for tunneling ionization:
- Keldish, Sov. Phys. JETP **20**, 1307 (1965).
- Ammosov, Delone and Krainov, Sov. Phys. JETP **64**, 1191 (1986).
- Result is an ionization probability rate
- Taken from Eq. (1) of ADK paper
- Presented here in convenient units
- W=1 would imply 100% ionization in 1 s, assuming constant E

- E is the local electric field magnitude
- i  is the ionization energy
- n*  3.69 Z / i1/2 [eV] is the “effective” principal quantum number
- Z is the charge state of the resulting ion (Z=1 for neutral atom)

## ADK Implementation – details & validation

- Details:  here we tabulate i, Z and n* for H, He, Li and Cs:
- Validation:  simulations with He and He+ are compared with data
- The l’OASIS group at LBNL (Wim Leemans *et al*.) uses ionization-induced blue shift measurements routinely as a diagnostic for their laser pulses
- We modeled one data set with OOPIC and compared the amount of blue shift seen in the code with that seen in the experiments, obtaining good agreement
- D.A. Dimitrov, D. Bruhwiler, W.P. Leemans, E. Esarey, P. Catravas, C. Toth, B. Shadwick, J.R. Cary and R. Giacone, Proc. Advanced Accel. Concepts Workshop (AIP, New York, 2002), Vol. **647**, p. 192.

## A shorter (higher-density) e- drive beam recovers first peak in Ez 

- 50 GeV e- drive beam is now half as long
-  r=20 m & z=30 m
- 2x1010 e- in the bunch
- Variables r & z are normalized to e=282 m
- neutral Li density is nLi=1.4x1016 cm-3
- thus, the peak e- density is ne=nLi
- up to 27 Li+/e- pairs are created in each cell where ionization occurs
- The fields are normalized to E0=11.4 GV/m
- first peak in Ez is greater than E0, which indicates a nonlinear response
- the wake then rapidly loses coherence

## Tunneling Ionization Effects for E-164 and E-164x Parameters

- We conducted parameter studies for Li and Cs
- Presented at 2003 Orion workshop prior to start of E-164
- D.A. Dimitrov, D. Bruhwiler, R. Busby, J.R. Cary, W.P. Leemans  and E. Esarey, “Parameter Studies of Tunneling Ionization Effects in E-164 with Cs and Li -- A Use Case of the IONPACK Software Library”
- Showed that ionization would be problematic for E-164 and that pre-ionization would not be necessary for E-164x
- Benchmarking of OOPIC and OSIRIS
- Facilitated by collaboration through the DoE SciDAC initiative
- Accelerator simulation project funded by HEP/NP offices
- Advised S. Deng during her initial implementation of tunneling ionization into OSIRIS and carefully benchmarked the two codes
- good agreement was obtained
- We then looked more carefully at positron wakes

## 2-D OOPIC simulations show good agreementwith previous (Lee et al., 2001) 3D PIC results 

- Ez surface plot, e-
- Ez lineout, e-

- Ez surface plot, e+
- Ez lineout, e+

## Optimal Plasma Density from Linear Response

- Wake field on axis (linear response theory) from relativistic drive beam with bigaussian density distribution
- S. Lee, T. Katsouleas, R.G. Hemker, E.S. Dodd and W.B. Mori, Phys. Rev. E **64**, R045501 (2001).
- For fixed  r and z the optimal density is determined from:
-                   ;  for narrow beams (kpr << 1)
-                   ;  for r = z
- and in the general case from:
- D. Bruhwiler, D.A. Dimitrov, J.R. Cary, E. Esarey and W.P. Leemans, Proc. Part. Accel. Conf. (2003), p. 734.

## Positron wakes in neutral Cs (with TI) are very similar to the idealized case of a pre-ionized plasma

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

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

## Beam and plasma diagnostics for e+ wake with TI

- e+ beam (scatter plot)
- electrons from TI of Cs

- e+ beam (density plot)
- TI electrons (density plot)

## Same diagnostics for e+ wake in a pre-ionized plasma

- e+ beam (scatter plot)
- plasma electrons (scatter plot)

- e+ beam (density plot)
- plasma electrons (density plot)

## Dependence of Peak Electric Field on Axis and Its Location Relative to the e+ Beam on Plasma/Gas Density

- Peak accelerating field depends weakly on the plasma/gas density in an extended interval around the optimal density from linear response theory

- Peak field position relative to center of the positron beam – approximate location for witness bunch – decreases as density increases

## Dependence of  Ekink on Axis and Its Location Relative to the e- Beam on Plasma/Gas Density

- Ekink (max field, just before the spike) depends weakly on the plasma/gas density in an interval around the optimal density from linear theory

- Ekink field position relative to center of the electron beam – approximate location for witness bunch –  distances are larger than for e+ beams

## VORPAL – Laser Pulse in Channel w/ Field Ionization of He

- Ex

- Ez

- ne

- nHe

- nHe+

- nHe++

## VORPAL scales well up to 4,000 processors at NERSC

**VORPAL scales well up to 4,000 processors at NERSC**

## Conclusions

- OOPIC/IONPACK simulations showed in early 2003 that one could use neutral Cs gas for E-164x parameters
- Confirmed by exciting new results coming out of E-164x
- For E-164x parameters, the results with TI of neutral Cs are very close to the ideal case of a pre-ionized plasma
- Peak fields in TI case are slightly higher
- Peak fields for e- drivers are ~2x higher than for e+ drivers
- The gas density can be varied to modify the separation between e+ drive and witness beams
- cost in terms of reduced gradient is modest
- for e+ drivers, optimal separation is 30 – 35 m
- for e- drivers, the optimal separation is 75 - 175 m
- Now moving from OOPIC to VORPAL, via IONPACK
- Faster particle push, massively parallel, 3D
- VORPAL team:  J. Cary, C. Nieter, P. Messmer, D. Dimitrov,            R. Busby, P. Stoltz, J. Carlson, D. Bruhwiler