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Ionization Physics in Plasma Wakefield Accelerators

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

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Ionization Physics in Plasma Wakefield Accelerators

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  1. Ionization Physics in Plasma Wakefield Accelerators D. Bruhwiler,1D.A. Dimitrov,1 J.R. Cary,1, 2 W.P. Leemans,3 and E. Esarey,3 C. Nieter1 1. Tech-X Corporation 3. Lawrence Berkeley National Laboratory 2. University of Colorado Tech-X Corporation 5621 Arapahoe Ave., Suite A Boulder, Colorado 80303 http://www.txcorp.com • 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)

  2. 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.

  3. 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)

  4. Parameters for 2-D (r,z) “(SLC) Afterburner” Simulations(without tunneling ionization) • 50 GeV e- drive beam • sr=20 mm & sz=63 mm • 2x1010 e- in the bunch • r,z are normalized to le=282 mm • e- density is ne=1.4x1016 cm-3 • Grid size is Dz=Dr=7.5 mm • 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

  5. 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 xi 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)

  6. ADK Implementation – details & validation • Details: here we tabulate xi, 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.

  7. A shorter (higher-density) e- drive beam recovers first peak in Ez • 50 GeV e- drive beam is now half as long • sr=20 mm & sz=30 mm • 2x1010 e- in the bunch • Variables r & z are normalized to le=282 mm • 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

  8. 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

  9. 2-D OOPIC simulations show good agreementwith previous (Lee et al., 2001) 3D PIC results Ez surface plot, e- Ez lineout, e- Ez surface plot, e+ Ez lineout, e+

  10. 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 sr and sz the optimal density is determined from: • ; for narrow beams (kpsr << 1) • ; for sr =sz • 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.

  11. 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)

  12. Beam and plasma diagnostics for e+ wake with TI e+ beam (density plot) TI electrons (density plot) • e+ beam (scatter plot) • electrons from TI of Cs

  13. 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)

  14. 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

  15. 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

  16. VORPAL – Laser Pulse in Channel w/ Field Ionization of He Ex Ez ne nHe++ nHe nHe+

  17. VORPAL scales well up to 4,000 processors at NERSC

  18. 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 mm • for e- drivers, the optimal separation is 75 - 175 mm • 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

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