# Presentation: 796177

## Self-consistent simulations of particle beam/plasma interaction with its environment

**Heavy Ion Fusion Science Virtual National Laboratory**
**Lawrence Berkeley National Laboratory**
- DOE OFES Theory Seminar Series
-  June 5, 2007

**Self-consistent simulations of particle beam/plasma interaction with its environment**

- Vay - OFES TCC 07

## Collaborators

**M. A. Furman, C. M. Celata, P. A. Seidl, K. Sonnad**
**	*****Lawrence Berkeley National Laboratory***
**R. H. Cohen, A. Friedman, D. P. Grote, **
**M. Kireeff Covo, A. W. Molvik, W. M. Sharp**
**	*****Lawrence Livermore National****** Laboratory***
**P. H. Stoltz, S. Veitzer**
**	*****Tech-X Corporation***
**J. P. Verboncoeur **
**	*****University of California - Berkeley***

- Vay - OFES TCC 07

## Outline

**Context**
**Simulation tools**
**Benchmarking against experiments**
**Application to high energy physics**
**Summary**

- Vay - OFES TCC 07

## Context

## Today’s HIFS program is directed at beam & Warm Dense Matter physics in the near term, and IFE in the longer term

**The physics of compressing beams in space and time**
**-- Drift compression and final focus**
**-- High brightness beam preservation**
**-- Electron cloud, beam halo, non-linear processes**** **
**Warm Dense Matter (WDM) experiments**
**-- Equation of state**
**-- Two-phase regime and droplet formation**
**-- Insulator and metals at WDM conditions**
**Hydrodynamics experiments relevant to HIF targets**
**-- Hydrodynamic stability, volumetric ion energy deposition,                            and Rayleigh-Taylor mitigation techniques**

**Today’s HIFS program is directed at beam & Warm Dense Matter physics in the near term, and IFE in the longer term**

- Vay - OFES TCC 07

## It is highly desirable to minimize the space between the beam and the accelerating structure.

- (from a WARP movie; see http://hif.lbl.gov/theory/simulation_movies.html)

-  This elevates the likelihood of "halo" (outlier) ions hitting structures, ...

- ... so that a detailed understanding is needed.

- Vay - OFES TCC 07

**Notes:**
Show movie.

## Sources of electron clouds

** ****ion induced emission from**
** ****expelled ions hitting vacuum wall**
** ****beam halo scraping**

**Sources of electron clouds**

_**Primary:**_
_**Secondary:**_

*i**+*	= ion* *
*e**-**	*= electron
- g 	= gas
- = photon
- 	= instability

***Positive***
***Ion Beam***

***Pipe***

** ****Ionization of **
** ****background gas **
** ****desorbed gas**

** ****secondary emission from electron-wall collisions**

*e**-*

** ****photo-emission from synchrotron radiation (HEP)**

******

- Vay - OFES TCC 07

## Simulation goal - predictive capability

- Source-through-target **self-consistent** time-dependent 3-D** **simulations of beam, electrons and gas with self-field + external field (dipole, quadrupole, ...).

**WARP-3D**
**T = 4.65********s**

***200mA ***
***K******+***

**       ****Electrons**

**From source...**

**...****to target.**

**HCX**

- Vay - OFES TCC 07

## Simulation tools

## WARP is our main tool

**3-D accelerator PIC code**** **
**Geometry:****	****3D****, (x,y), or (r,z)**
**Field solvers:****    ****FFT, capacity matrix, multigrid**
**Boundaries:****     ****	****“cut-cell” --- no restriction to “Legos”**
**Bends:     ****	****“warped” coordinates; no “reference orbit”**
**Lattice:     ****	****general; takes MAD input**
**solenoids, dipoles, quads, sextupoles, ...**
**arbitrary fields, acceleration**
**Diagnostics:     Extensive snapshots and histories**
**Parallel:****     ****MPI**
**Python and Fortran:**** “steerable,” input decks are programs **

- Vay - OFES TCC 07

## WARP-POSINST has unique features 

**WARP-POSINST has unique features **

**  ****merge of WARP & POSINST**

- Vay - OFES TCC 07

## re-diffused

**Monte-Carlo generation of electrons with energy and angular dependence.**
**Three components of emitted electrons:**
- backscattered:
- rediffused:
- true secondaries:

- true sec.

- back-scattered
- elastic

**POSINST provides advanced SEY model. **

*I**0*

*I**ts*

*I**e*

*I**r*

**Phenomenological model:**

-  based as much as possible on data for ** and *d****/dE*
-  not unique (use simplest assumptions whenever data is not available)
-  many adjustable parameters, fixed by fitting ** and *d****/dE* to data

## We have benefited greatly from collaborations

-  ion-induced neutral emission developed by J. Verboncoeur (UC-Berkeley).

**We have benefited greatly from collaborations**

- Vay - OFES TCC 07

## Benchmarking against experiments

## Benchmarked against dedicated experiment on HCX

- Capacitive
- Probe (qf4)

**Clearing electrodes**

**Suppressor**

***K******+***

**e****-**

**Short ****experiment => need to ****deliberately amplify**** electron effects: **let beam hit end-plate to generate copious electrons which propagate upstream.** **

**End plate**

**INJECTOR**

**MATCHING**
**SECTION**

**ELECTROSTATIC**
**QUADRUPOLES**

**MAGNETIC**
**QUADRUPOLES**

**Benchmarked against dedicated experiment on HCX**

- Retarding  Field Analyser (RFA)

**Location of Current**
**Gas/Electron Experiments**

- GESD

**1 MeV, 0.18 A, t ≈ 5 ********s, ****6x10****12**** K****+****/pulse, 2 kV space charge, tune depression ****≈**** 0.1**

- Vay - OFES TCC 07

## Comparison sim/exp: clearing electrodes and e- supp. on/off

***simulation***

***200mA K******+***

**e****-**

** ****0V                       0V                      0V                       V=****-10kV****, ****0V**

**Comparison sim/exp: clearing electrodes and e****- ****supp. on/off**

- Time-dependent beam loading in WARP from moments history from HCX data:
-  current
-  energy
-  **reconstructed **distribution** **from XY, XX', YY' slit-plate measurements

**(a)**

**(b)**

**(c)**

**Good semi quantitative agreement.**

- measurement

- reconstruction

- Vay - OFES TCC 07

## Detailed exploration of dynamics of electrons in quadrupole 

**Importance of secondaries                         **- if secondary electron emission turned off:
**run time ~3 days **
**	**- without new electron mover and MR, run time would be ~1-2 months!

**Detailed exploration of dynamics of electrons in quadrupole **

- WARP-3D
- T = 4.65s

**Oscillations**

**Beam ions hit end plate**

**e****-**

**0V               0V           0V/+9kV              0V**

**Q4**

**Q3**

**Q2**

**Q1**

***200mA K******+***

***200mA ***
***K******+***

**       ****Electrons**

- _x0003__x0016_

**(c)**

**0.            2.      time (********s)       6.**

**0.**
**-20.**
**-40.**

**I (mA)**

**Potential contours****	**

**(c)**

**0.            2.      time (********s)       6.**

**I (mA)**

**0.**
**-20.**
**-40.**

**Electrons **
**bunching**

**~6 MHz signal in ****(C)**** in simulation AND experiment**

- WARP-3D
- T = 4.65s

- Vay - OFES TCC 07

## Quest - nature of oscillations

**Quest - nature of oscillations**

**Progressively removes possible mechanisms **
**Not ion-electron two stream**

- R (m)

- V(m/s)

- Fluid velocity vectors
- (length and color according to magnitude)

- Vortices?

- Shear flow

- color according to magnitude of velocity

- Other mechanisms:
-  	Virtual cathode oscillations
-  	-Density-potential, 		feedbacks to drift velocity
-  	Kelvin Helmholtz/Diocotron 		(plausible, shear in drift velocities)

- Vay - OFES TCC 07

## Application to high energy physics

## HEP e-cloud work currently uses “quasi-static” approximation

- A 2-D slab of electrons (macroparticles) is stepped backward (with small time steps) through the beam field and 2-D electron fields are stacked in a 3-D array, that is used to push the 3-D beam ions (with large time steps) using maps (as in HEADTAIL-CERN) or Leap-Frog (as in QUICKPIC-UCLA), allowing direct comparison.

- 2-D slab of electrons

- 3-D beam

- s

- s0

- lattice

- Vay - OFES TCC 07

## Quasi-static mode (QSM) has been added to WARP

**Rationale****  - we had the building blocks****  - we need to reproduce HEP codes results for meaningful comparisons**** ****Comparison WARP-QSM/HEADTAIL on CERN benchmark**

- Vay - OFES TCC 07

## WARP/POSINST applied to High-Energy Physics

**LARP funding: simulation of e-cloud in LHC **
**	****Proof of principle simulation: **
**Fermilab: study of e-cloud in MI upgrade (K. Sonnad)**
**ILC: study of e-cloud in positron damping ring wigglers (C. Celata)**

**Quadru****poles**
**Drifts**
**Bends**

**WARP/POSINST-3D - t = 300.5ns**

**1 LHC FODO cell (~107m) - 5 bunches - periodic BC (04/06)**

- Vay - OFES TCC 07

## How can FSC compete with QS? Recent key observation: range of space and time scales is not a Lorentz invariant*

- same event (two objects crossing) in two frames
- 	Consequences
- there exists an optimum frame which minimizes ranges,
- for first-principle simulations (PIC), cost*T/****t* ~ 2 (*L/l*T/****t* ~ 4 w/o moving window),

***J.-L. Vay, PRL 98, 130405 (2007)**

**for ****large**** ********, potential savings are ****HUGE****!**

- = (*L/l, T/****t*)

- 0

- 0

- 0

- 0

- 0

**Range** of space/time scales =(*L/l,T/****t*) vary continuously as **2**********

- space

- space+time

- F0-center of mass frame            FB-rest frame of “B”

- Vay - OFES TCC 07

## Free electron lasers

**Free electron lasers**

**HEP accelerators (e-cloud)**

- 1nm

- 10km

- 10m

- 10cm

**Laser-plasma acceleration**

- x1000

- 3cm

- 1m

- In laboratory frame.
- longitudinal scale  x1000/x1000000...

- ... so-called “multiscale” problems
- = very challenging to model!
- Use of approximations
- (quasi-static, eikonal, ...).

**A few systems which might benefit include...**

- x1000000

- x1000

- 10km/10cm=100,000.

- 10m/1nm=10,000,000,000.

- 3cm/1m=30,000.

- Vay - OFES TCC 07

## Lorentz transformation => large level of compaction of scales

**Lorentz transformation => large level of compaction of scales**

**HEP accelerators (e-cloud)**

**Laser-plasma acceleration**

**Free electron lasers**

- Vay - OFES TCC 07

**Notes:**
LPWA: frame at group velocity of laser in plasma in lab frame (standing wave in boosted frame)
FEL: bucket frame

## Speedup x1000

**Boosted frame calculation sample****proton bunch through a given e****–**** cloud***

**This is a proof-of-principle computation:**
**hose instability of a proton bunch**
**Proton energy: ********=500 in Lab**
** ****L= 5 km, continuous focusing**

- electron
- streamlines

- beam

- proton bunch radius vs. z

**CPU time:**
** ****lab frame: ****>2 weeks**
** ****frame with ********2****=512: ****<30 min**

**Speedup x1000**

***J.-L. Vay, PRL 98, 130405 (2007)**

- Vay - OFES TCC 07

**Notes:**
Beam (in laboratory): 
1012 protons,  = 500, Gaussian profile 
sigx==1mm,=10 cm,
x=y=100m, 
vthx=vthy=vbeam/x; vthz=0,
initial offsets: 
x=0.1, vy=0.1vthy.

Electron background (in laboratory):
Nmax=1015 m-3,
L=5 km:
2 km linear ramp up,
1 km flat top,
2 km ramp down.

Beamline (in laboratory):
Cylindrical pipe, r=1 cm,
External azimuthal magnetic field B=0.15 (T/m)r 

WARP run-times on 2 nodes  (8 procs) of HIF-VNL cluster “Fusion”:
Lab frame: >2 weeks,
Frame 2=512: <30min.

## Summary

**WARP/POSINST code suite developed for HIF e-cloud studies**
**Parallel 3-D AMR-PlC code with accelerator lattice follows beam **_**self-consistently**_** with gas/electron generation and evolution,**
**Benchmarked against HCX**
_**highly instrumented**_** section dedicated to e-cloud studies,**
**Being applied outside HIF/HEDP, to HEP accelerators**
**found that cost of self-consistent calculation is greatly reduced in **_**Lorentz boosted frame (with **__****__**>>1)**_**, thanks to relativistic contraction/dilatation bridging space/time scales disparities,**
**1000x speedup demonstrated on proof-of-principle case,**
**will apply to LHC, Fermilab MI, ILC.**

- Vay - OFES TCC 07