# Presentation: 468338

## Beam Modeling Progress

**Beam Modeling Task Area Leader**
**HIF-VNL Q4 Progress Report Meeting**
**September 29, 2004**

**Beam Modeling Progress**

**Heavy Ion Fusion         Virtual National Laboratory**

**Notes:**
This slide shows a cartoon of a full-scale heavy ion fusion accelerator and fusion-chamber system, indicating the key elements along the beam line. A real system would have ~100 beams (too many to draw here!) 
The ultimate goal is inertial fusion energy; the nearer-term goals center on beam physics and high-energy density physics studies in heated targets
The HIF-VNL is a collaboration among LBNL, LLNL, and PPPL (Ron Davidson’s group), along with collaborators in industry and academia.

##      Outline

**Modeling in support of experimental milestones**
**Injector research**
**High-current transport: HCX & electron clouds**
**Neutralized transport & focusing: NTX**
**Preparations for future experiments**
**Other developments & closing thoughts**
**	*****Embedded: computational physics innovations***

## I. Modeling in support of experimental milestones

**a) Injector research****Goal:  Carry out full voltage beamlet acceleration and determine beamlet characteristics (multibeamlet source configured in FY 2003) for heavy ion beam inertial fusion.**

## High-gradient beamlet merging experiment (with initially parallel beamlets) is in progress on STS-500

**WARP simulations show that the beamlets expand as they merge**

**The emittance growth saturates as the beamlets begin to touch each other**

**Normalized emittance (x and y)**

**Comparisons of data with simulations will be carried out**

**High-gradient beamlet merging experiment (with initially parallel beamlets) is in progress on STS-500**

** ****(Simulations by D. Grote)**

## WARP guided the design of the “curved-plate” beamlet-merging experiment that is planned for FY05 on STS-500

**119 beamlets, I****Total**** = 0.07 A, E****final**** = 400 keV**

**Normalized emittance**

**RZ and XY for synthesis; 3D for validation**

**WARP guided the design of the “curved-plate” beamlet-merging experiment that is planned for FY05 on STS-500**

** ****(Simulations by D. Grote)**

## WARP simulations of HCX triode illustrate a new capability: the merger of particle-in-cell (PIC) & adaptive mesh refinement (AMR)

- N (-mm.mrad)

- Z(m)

**The VNL’s development of AMR/PIC is a significant contribution to computational physics**

**This example:**
**	****~ 4x savings in computational cost**
**(in other cases, far greater savings) **

**WARP simulations of HCX triode illustrate a new capability: the merger of particle-in-cell (PIC) & adaptive mesh refinement (AMR)**

** ****(Simulations by J-L. Vay)**

**r**

**z**

## Adaptive Mesh Refinement requires automatic generation of nested meshes with “guard” regions 

**Simulation of diode using merged Adaptive Mesh Refinement & PIC**

## WARP simulations of STS-500 experiments clarify our understanding of short-rise-time beam generation

**Current (mA) at Faraday cup**

**Result depends critically on mesh refinement**

**6**

**4**

**2**

**0**

**time (********s)**

**0**

**2**

**4**

**WARP simulations of STS-500 experiments clarify our understanding of short-rise-time beam generation**

**5-cm-radius K****+**** alumino-silicate source **

## b) High-current transport: HCX & electron cloudsGoal:  Evaluate the effects of stray electrons on heavy ion beams by comparing results from the high current experiment (HCX) with calculations of beam transport through HCX

**I. Modeling in support of experimental milestones**

## HCX experimental configuration includes magnetic quadrupoles, with clearing and suppressor electrodes

**HCX experimental configuration includes magnetic quadrupoles, with clearing and suppressor electrodes**

**Quadrupole magnets (MA1-MA4) have elliptical bores (6 and 10 cm major axes)**

**beam**

**clearing electrodes**

## WARPxy 2D simulations initiated with measured (a,a,b,b) yielded new beam “tune”  for HCX

- Magnet aperture

**y (mm)**

- PIC statistical edge

- Expt data (2x RMS)

**+**

**+**

**WARPxy 2D simulations initiated with measured (a,a********,b,b********) yielded new beam “tune”  for HCX**

**z (m)**

**x  (mm)**

**HCX ion dynamics**

**+**

**+**

## HIF-VNL’s research into “electron clouds” & gas is addressing a major issue for ion accelerators

**Electron cloud effects (ECEs) impact:**
**HIF accelerators (for HEDP and/or IFE)**
**present electron-positron colliders and ion rings (e.g. PSR)**
**next generation colliders and ion rings (NLC, LHC, SNS, GSI)**
**Collaboration with Tech-X (2 SBIR’s), U.C. Berkeley, LBNL/HEP**

**electron cloud**

**Invited papers: **
**3**** at ECloud04**
**3**** at other conferences **
**Future:**** ****1**** at APS-DPP & ****1**** at PAC**
**•****	****Computational advances have broad applicability**
**•****	****Expect at least 5 refereed publications from FY04 work**

## Experiments and simulations explore sources, sinks, and dynamics of stray electrons

- beam

**Experiments and simulations explore sources, sinks, and dynamics o****f stray electrons**

**Notes:**
Secondary electrons are “born passing” — 
nonadiabaticity can raise ne by O(100), but e-e 2-stream appears minor
Electrons from neutrals are “born trapped” — 
uncertainty in neutral emission & ionization cross-section is significant 

## Toward a self-consistent model of electron effects

**Roadmap for self-consistent electron physics modules for WARP**
**Key: ****operational; **** ****implemented, testing;**** ****partially implemented;**** ****active offline development (as of 9/04)**

## Simulation using imposed (frozen) electron distributions show that the beam is surprisingly robust; but resonant behavior may be important

**Simulation using imposed (frozen) electron distributions show that ****the beam is surprisingly robust****; but resonant behavior may be important**

**Random amplitude variation:**
**2.1% beam loss**

**WARP ion beam simulations**
- 450 m (200 quads) of transport

**Sinusoidal shape variation**
**28% beam loss**

**<n****e****>/n****b**

**RMS n****e**** variation**
**= mean n****e**

**%**

**Notes:**
I = 0.81 Amp
2 MeV
Drifting
From Ron Cohen
Hlp = 45 cm/2
100 lattice periods
A=38.96
“Random” has random amplitude of electrons from 0-20% of the beam density, mean=10%.  Random shape and other ways of inserting randomness of the electron distribution were not as virulent.
Sinusoidal has ne/nb=10%.

wave number norm’d to inverse lattice period

## A sequence of simulations gave us a first picture of wall-desorbed electron density distributions in quads

**minimum**

**Ran WARP with mismatch; noted where ions hit walls**
**Then launched electrons at wall using prescription derived from exp’ts**

**A sequence of simulations gave us a first picture of wall-desorbed electron density distributions in quads**

**(log scale)**

**Inclusion of first-flight reflected ions yields electrons at ~ 45°**

- accumulated electron density

**scattering**

**peak**

**Electrons confined close to birth positions on non-penetrating field lines**

- accumulated electron density

## Large time-step “interpolated” electron mover should have applications in MFE, astrophysics, space physics, ...

**Ron Cohen will present this work in an invited talk at APS-DPP 2004**

**Full-orbit, ********t = 0.25 / f****ce**

**New mover, ********t 25x larger**

**Spatial distribution of electrons from a source uniform out to nominal r****b**** (an approximate model for electrons produced by ionization of gas)**

## Experimental (HCX) observations: without suppressor or clearing electrodes, electrons distort phase space (“Z-ing”)

**Experimental (HCX) observations: without suppressor or clearing electrodes, electrons distort phase space (“Z-ing”)**

- 1 MeV, 0.18 A K+ ion beam after 4 quadrupole magnets

- 409220120

**Beam emerging from slit (see diagram on left) shows 3 components of v****x**

****

- 409220222-409220257

- 409220100 - 409220138

**Measured x vs. x******

- Slit

**x******

**x**

**x**

**y**

**Notes:**
Where does the slit really go?  I’ve invented a place that looks like it will make 3 components.  Is that OK?
I need to read the milestone paper, but Ron, Jean-Luc, Alex-- should I add or subtract something to/from what I’ve written in the box?

## A “z” or “s” distortion of phase space can result in multiple stripes in the image of a beam that has passed through a slit

- X

- X ́

- X

- Y

- Image

- Slit allows only particles having x in this range to pass through

## When the electron backflow from the end plate in HCX    is suppressed, the beam is observed to be well-behaved

- image after passage thru slit

- f(x,x ́) derived from multiple slit positions

**x******

**x**

**x**

**y**

## 3-D WARP simulations treat (for the first time) electrons self-consistently, using new large-timestep mover

- Electrons (shown in red) can only enter two quadrants of the final quadrupole

- End-on view at z = 4.0 m, t = 4.0 s

- Side-on view at x = 0, t = 4.0 s

- Their flow tracks equipotentials (blue) until they strike the wall (reemission not used in this run)

## 3-D simulation w/o e– re-emission results in electrons confined to the 4th magnet.  Reemission reinforces Z-ing.

- X’

- X’

- X’

- X’

***No***** electrons**

***With***** electrons **
**(no reemission)**

**A run with secondary emission is under way**

- X’

- X’

**3-D**** simulation w/o e****–**** re-emission results in electrons confined to the 4th magnet.  Reemission reinforces Z-ing.**

- X

- X

***With***** electrons **
**& reemission**

**(Beam hits plate at 1 ********s)**

- X’

- X

**2.4 ********s**

## Hi-resolution 2D (r,z) XOOPIC runs were carried out at UCB, studying the region between the final quad and the end

- Virtual cathode forms near emitting surface; energetic electrons make it through
- Over time, the phase space hole fills in and the virtual cathode grows deeper
- These runs inform WARP 3D runs, which have used lower resolution (AMR is planned)

**Hi-resolution 2D (r,z) XOOPIC runs were carried out at UCB, studying the region between the final quad and the end**

- virtual cathode

- t=0.2 s

- t=2 s

- t=2 s

- vz (m/s)

- vz (m/s)

-      0                    z (m)               0.26

**Notes:**
972 keV, 174 mA, 22 mm K+ beam
 26 cm x 11 cm grounded cylinder

## c) Neutralized transport & focusing: NTXGoal:  Integrate elements of initial plasma neutralized beam focus and carry out initial experiments in support of heavy ion beam   inertial fusion

**I. Modeling in support of experimental milestones**

## After 4 magnetic focusing quads, data & WARP-generated density profiles agree well, except for halo;  still +/- 3% uncertainty in B ́/energy ratio

**265keV**

**283keV**

- Vertical

- Horizontal

- Vertical

- 1.5 mA beam

- Horizontal density
- profile

**After 4 magnetic focusing quads, data & WARP-generated density profiles agree well, except for halo;  still +/- 3% uncertainty in B ́/energy ratio**

**Notes:**
What has been adjusted to make these profiles agree?  Did you adjust the energy in the simulations?  By how much?  Is the amount of the adjustment within the error bar you gave on B'/(B*rho), given that the energy you ran the simulations with, as I recall, was wrong by 3% from what was measured? (What I remember is that you changed the energy by 3% to get agreement.  You assumed that the energy was off by that much.  But measuring the energy showed that the energy was wrong in the opposite direction by about 3%,giving an error that was the equivalent of a 6% error in energy between the data and theory.  That would correspond to a 3% error in B.  So am I correct that that is just equal to the error bar you estimate for B?

## LSP simulations of NTX transport are now being initialized with the measured 4D particle distribution 

**LSP fluence at target**

**Carsten Thoma, et. al.**

**EM, 3D cylindrical geom., 8 azimuthal spokes**
**3 eV plug 3x10****9**** cm****-3****, volume plasma 10****10**** cm****-3**

**Notes:**
Ring electrode driven by 5 kV TEM wave
2 days run time on 4 processors

## LSP simulations agree with experimental data at focal plane for different neutralization methods (within error bars)

**MEASUREMENT**

**SIMULATIONS**

- With plasma plug

- With plasma plug
- and RF Plasma

- “No space charge”

**MEASUREMENT**

**SIMULATION**

**MEASUREMENT**

**SIMULATION**

**MEASUREMENT**

**SIMULATION**

**1.3**

**1.7 mm**

**1.1**

**1.4 mm**

**0.8**

**1.0 mm**

**Radius containing**
**1/2 the integrated**
**current is given**

**6 mA**
**10 mm initial radius**

**0**

**1**

- Linear
- scale

## II. Preparations for future experiments

## Strategy: maximize uniformity and the efficient use of beam energy by placing center of foil at Bragg peak

**Ion beam **

**In simplest example, target is a foil of solid or “foam” metal**

**Example: He**

**Enter foil**

**Exit foil**

******dE/dX ******** ********T**

**log-log plot => fractional**
**energy loss can be high**
**and uniformity also high**
**if operate at Bragg peak**
**(Larry Grisham, PPPL) **

**Energy**
**loss rate**

**Energy/Ion mass**

**(MeV/mg cm****2****)**

**(MeV/amu)**

- (dE/dX figure from L.C Northcliffe
- and R.F.Schilling, Nuclear Data Tables,
**A7**, 233 (1970))

## We have looked at the effect of a velocity spread on temperature uniformity on target

**We have looked at the effect of a velocity spread on temperature uniformity on target**

**1.8 %**

**10%**

**6.3%**

**4.0%**

**2.5%**

**15.9%**

**Log[*****v/v***]**

**Log[*****T/T***]**

## October workshop will further develop new concepts for achieving ion-driven HEDP

**First step is to derive requirements on accelerator**
**Stopping power as function of ion mass and energy**
**Range over which variation in stopping power is tolerable**
**Ionization state of target, allowing calculation of energy density, pressure, and temperature **
**Simple Zeldovich and Raizer model used for equation of state**
**Velocity spread for which combined ion stopping power is within tolerable limits**
**Objects of workshop:**
**Develop target and diagnostic concepts**
**Requirements depend on suite of diagnostics envisioned.**
**Develop accelerator concepts**
**Experiments may optimize differently for different accelerators**

## LSP simulations of neutralized drift and focusing show possibility of strong compression in NDCX-1

**As simulated:**
**Axial compression ****120 X**
**Radial compression to 1/e  focal spot radius ****< 1 mm**
***Beam intensity on target increases by 50,000 X*****.**

**R(cm)**

**3.9T solenoid**

**Z(cm)**

**LSP simulations of neutralized drift and focusing show possibility of strong compression in NDCX-1**

**(simulations by Welch, Rose, Henestroza, Yu) **

**Ramped 220-390 keV, K****+****, 24 mA ion beam injected into a 1.4-m long plasma column with density 10 x beam density. **

## Simulation of a scaled experiment: novel High Line Charge Density Injector (NDCX-1c) 

**Gun**

**Acc.**

**column**

**Solenoid**

**transport**

**(Fully self-consistent WARP3D calculation of an ACCEL-DECEL-LOAD-AND-FIRE SYSTEM)**

**Simulation of a scaled experiment: novel High Line Charge Density Injector (NDCX-1c) **

## NDCX-2 beam compresses to conditions of interest for HEDP

- Time-Integrated
- Energy Deposition

**NDCX-2 beam compresses to conditions of interest for HEDP**

**< 1 ns, < 1 mm pulse “on target” at z = 152 cm**
**Compressed to .75 kA, 75x**

- (Simulations by    C. Thoma, MRC)

**Notes:**
Sol42

C.T. just emphasize current compression and radius

## Several Neutralized Drift Compression issues addressed

**Several Neutralized Drift Compression issues addressed**

**Plasma neutralization allows 50-100x compression with applied velocity tilt**
**Two-stream impact on beam is small **
**Filamentation minimized for r****c****/********sd**** << 1,    n****p**** >> n****b**
**Transition from Brillouin flow to NDC is feasible with dipole B**
**2-stage focusing with solenoid and discharge channel transversely focuses a beam with large energy tilt**
**NDC can be tested on proposed NTX experiment w; large energy tilt; runs show condition approaching HEDP possible given 0.1% velocity accuracy**

- Time-Integrated Energy Deposition for NTX Phase 2 (LSP)

- 100 ns

- 60 ns

- 140 ns

- 20 ns

- Solenoid focusing in plasma

**Key unaddressed issues:**
**Plasma must be created in varying solenoidal fields**
**Beam stripping by plasma limits NDC length**
**Multiple beam combining for driver**

**Notes:**
C.T. need to emphasize that you get to HEDP regime with prescribed velocity accuracy

## NDCX-3 experiments may employ a novel accelerating method based on a Traveling Wave Accelerator

**Beam “surfs” on traveling pulse of E****z**** (moving at ~ 0.01 c in first stage)**
***One possible configuration:***

**NDCX-3 experiments may employ a novel accelerating method based on a Traveling Wave Accelerator**

**A. Friedman to present an invited talk on accelerators for HEDP at PAC ’05 **

## III. Other developments           and closing thoughts

## Challenges are being addressed by new computational capabilities

**resolution challenges**** (Adaptive Mesh Refinement-PIC)**
**dense plasmas ****(implicit, hybrid PIC+fluid - LSP)**
**short electron timescales ****(large-********t advance)**
**electron-cloud & gas interactions ****(a “roadmap”)**
**slowly growing instabilities ****(********f for beams - BEST)**** **
**beam halo**** (advanced Vlasov)**

**Fundamental simulation progress**

## Vlasov innovations promise a route to efficient simulation   of low-density “halo” regions of phase space

****** **
**moving phase-space grid, based **
**on non-split**
**semi-Lagrangian advance**
****
**adaptive mesh**
**in phase space**

**Active collaboration with E. Sonnendrucker, Univ. Strasbourg**

## Closing thoughts ...

**Improvements in simulation capabilities over the past year were very significant, and offer benefits for a range of applications**

**Closing thoughts ...**

**These advanced tools are being employed in planning for the future, and are especially valuable in light of the new HEDP mission**