# Presentation: 532325

## Simulations of Neutralized Final Focus

- D. R. Welch, T. C. Genoni, D. V. Rose and C. Thoma
- Mission Research Corporation
- J. J. Barnard, E. Henestroza, P. K. Roy and S. S. Yu
- Lawrence Berkeley National Laboratory
- June 11, 2004
- 15th International Symposium on Heavy Ion Inertial Fusion
- Princeton University, Princeton NJ
- Work supported by the VNL for HIF through PPPL and LLBL

**Notes:**
25 minutes total for talks --- < 20 slides 
Thursday at 10:50

## Higher perveance beams possible with a modular solenoid driver* require neutralization to compress and focus

- Beam, plasma requirements for longitudinal compression in a plasma
- Beam-plasma instabilities
- Transition from Brillouin Flow (BF) to Neutralized Drift Compression (NDC)
- Transverse focusing in an immersed plasma
- Final Focus design for HIF driver
- NDC experiments with proposed NTX upgrade

- We examine NDC transport issues, transition, final focus and integrated transport

- *See W.I-12 Ed Lee

## LSP is used to examine in some depth NDC instability and transport issues

**NTX* **
**MEASUREMENT**

**L****SP**
**SIMULATIONS**

- With plasma plug

- With plasma plug
- and RF Plasma

- 100% neutralization

- With plasma plug

- With plasma plug
- and RF Plasma

- 100% neutralization

- LSP is being benchmarked in plasma neutralization experiments on NTX

- 6-mA, 254-keV, 2-cm K+ beam,  with *L* = 1m

- *See Th.I-5 P. Roy

## Required beam velocity tilt, accuracy

*L* increases with initial pulse length tp , 1/tilt

- velocity tilt for compression at position *L*

- e.g., 230 MeV, 210 ns Ne+ beam with 105-m drift length requires a 10% velocity tilt,
- 8 ns pulse requires ***v/v < *.36%

*t**min* is the minimum pulse time for error ***v/v*

**Notes:**
NDC requires accurate tilt and sufficient neutralized length 

## Plasma neutralization must be excellent

- The beam axial impulse due to space charge over the neutralized drift, *EL/<v>*, must be less than the applied velocity tilt*.* The neutralization fraction

- where *K(0)* is the initial beam perveance defined as *K* = 2*I**b**/I**A*2 with Alfven current *I**A **= **m**i**c*3/*eZ*.

- e.g. 780 A, 230 MeV, 20-cm radius, *K*(0) = 4x10-4 Ne+ beam with *L* = 105 m, then *f* > 0.995
-  *Consistent with NTX spot size  measurements for plasma neutralization of scaled beam*

- plasma plug
- and RF plasma

## 1D simulations of neutralization and impact of two-stream instability 

- 1D simulations of neutralization and impact of two-stream instability

- 780-A, 110-ns, 20-cm Ne+  beam with  *L* = 5450 cm
- 10% *v* tilt, random beam velocity variation  .1%
- nb = 109 cm-3 uniform np = 6x108 - 4x1010 cm-3
- z = 1⁄2 c / p , t = 1/5p  for all sims

- The most the beam can focus to is 40 kA due to the .1%  velocity variation (50x compression)

- Snapshots of beam phase space early and just before focus for **ballistic** transport showing effect of  applied velocity variation

- 200 ns

- 1200 ns

**Notes:**
Brill44_2sa – brill44_2sd  ,  ballistic with slowest v variation is brill44_2s

## Beam neutralization improves with plasma density

- L p /c > 5000 , tp p > 1000 for 4x1010 cm-3 plasma density
- Poor global neutralization at small plasma density limits pulse length
- Effect of 2 stream on beam is weak, produces longitudinal wings

- Beam current at focus

- Axial field near focus

**Notes:**
Runs brill42_2s0b, ab, bb, cb, db    with .001 random seed velocity 80% 90% > 99%, roughly 50 L omega_b/cbetas

## Two-stream impact on phase space

**2.5x10****9**** cm****-3**** density plasma**

**Ballistic transport**

**4x10****10**** cm****-3**** density plasma**

**1.0x10****10**** cm****-3**** density plasma**

- Too low a density results in space charge spreading
- Saturation of two stream growth leads to **tolerable **momentum spread

**Notes:**
Brill44_2s0b, etc

## Example: Focusing 150 kA, 230 MeV  Ne+ “combined” annular beam (K = 0.14) in plasma
Small but finite and nonlinear magnetic fields lead to beam filamentation, emittance growth
np >> nb and rc/sd < 1 yield best transport in LSP simulations and theory (W.P-14 I. Kaganovich)

- Small but finite and nonlinear magnetic fields lead to beam filamentation, emittance growth
*n**p** >> n**b* and rc/sd < 1 yield best transport in LSP simulations and theory (W.P-14 I. Kaganovich)

- Solenoidal field reduces growth rate of beam filamentation

- Uniform 10-cm beam

**Notes:**
Summary of run2d_20ab, run20_2kg and run20_8kg -  all higher resolution runs

## Beam matching possible from Brillouin Flow thru Neutralized Drift Compression

- Beam radius independent of energy in BF equilibrium with an energy tilt; *K*  ***L**2**a**2**/****2** c**2*, requiring constant* *line-charge **
- With perfect neutralization, matching for NDC is energy independent
*Transverse focusing in solenoid is energy dependent*

*with ****L**= eB/2****m, K* = 2*I**b **/I**A** **** **2*,  and *I**A* = *** mc*3/*eZ*

- Magnetized envelope equation

## Design considerations for transition from BF to NDC

- Beam in Brillouin Flow equilibrium abruptly transitions to NDC in immersed plasma
- At high K, the beam rotation is much too large once reaching the plasma  Bz must be reduced
- As in beamline simulations for NBT, the beam space charge draws in electrons from plasma
- dipole B field suppresses electron upstream motion*

- *Rose, Welch, Olson, Yu,  Neff, and the ARIES Team, "*Impact of beam transport method on chamber and driver design for heavy ion inertial fusion energy*," to appear in Fusion Science and Technology (2004).

## Transition region simulation with dipole B electron suppression

- 3D cylindrical LSP simulations with 1.2-4.8 kG dipole B fields
- 780 A, 20-cm, 8 -mm-mrad, 230-MeV, 110 ns Ne+1 beam (18 kJ)  with a 20% perfect energy tilt
- 1010 cm-3 plasma (10 nb)

- 2.5 T Bz falling to 0.125 T from 1-2.5 m

- What magnitude dipole field suppresses electron motion?

- Electron resupply at wall

- plasma

- Field chosen to give no net impulse or offset

- Ne+

**Notes:**
Brill_44-46

## 1.2-kG dipole field is insufficient

- Beam degradation seen in density due to anharmonic potential of backstreaming plasma electrons
- Electrons undergo corkscrew motion

- Log density

- Beam Density 10, 80 and 150 ns

- Plasma Electron Density

- Backstreaming electrons

**Notes:**
Brill_47 -  2 kG

## 4.8 kG field simulation shows no beam distortion or emittance growth

- plasma electrons are axially confined for over 110 ns

- Log density

- Beam Density 10, 80 and 150 ns

- Plasma Electron Density

**Notes:**
Brill_46 -  8 kG

## Energy acceptance of neutralized solenoidal focusing adequate for coupling to discharge 

*a**0** *and *a**f** *are the initial and final radius.

- Energy acceptance of neutralized solenoidal focusing adequate for coupling to discharge

- Factor of 10 compression permits Ef-E0/E = 0.25
- Beam emittance ultimately limits the maximum transverse focal length

- XXXXxxxxxxxxxxxxxxxXX

- Final Focus Solenoid

**Notes:**
Chromatic aberrations

## LSP shows nice transverse focusing in solenoid despite 20% energy tilt

- Log nb

- Example:
**Ne****+**** ions **
**780 A**
**230 MeV**
**20% E tilt**
**20-ns pulse**
***a***** = 10 cm **
**K = 10****-3 **

- Beam density reaches 3x1012 cm-3 by 140 ns, factor of 500 total increase
- Diamagnetic currents near focus modify Bz by < 2%
- Plasma heating near focus degrades beam in time
- Entire beam can be captured in discharge channel at 620 cm

- plasma density rises from 3x1011 to 3x1012 cm-3

**Notes:**
Plasma density is may not be high enough near focus, time-dependent heating of plasma, debye length 

## Integrated simulation of final focus design for NDC with discharge transport for HIF driver and NTX upgrade

- Plasma response (yellow and blue regions) modeled with a scalar conductivity in LSP

## 147 kJ beam energy transport design with 105 m drift length

- 3.35-kA, 10-cm, 8-mm-mrad, 231-MeV, 210 ns Ne+1 beam (147 kJ)  with a 20% perfect energy tilt to axially focus at L=104.5 m
- Injected Brillouin Flow equilibrium into 10 T
- Transition to neutralized drift (=1012 s-1) with .14 T at z = 2.4 m
- np/nb =10,  rL/sd  0.01 << 1 (no self fields)
- 5 kG dipole field at 2.2 m, no plasma electron transport
- Focusing solenoid at 90-100 m (2.7 T)
- 50-kA, discharge channel z>101 m: 2-0.5 cm radius in 1.5 m adiabatic channel; 3-m long, .5-cm radius straight channel

**Notes:**
Brill_48/long2d

## Beam couples well to hybrid target

- Filamentary growth does not degrade focus

- Log nb

**Notes:**
Scalar sigma model

## Good energy transport to target

- 92% of 147 kJ energy strikes target within 5 mm radius (Hybrid target)
- Halo forms from lack of “ears” and due to filamentation ( model dependent)

- Current rises to 140 kA at discharge

- Emittance remains small until focus

- Peaked distribution at target

- Well matched radius except for ends

## NDC Focusing on NTX Phase 1 

- K+ ions, 2-cm, 0.1 -mm-mrad, 24-mA initial current (0.02C/m), 400-ns, fast rise/fall current
- 220-390 keV --- 23% energy tilt with long. focus at 1.4 m
- 3.9-T uniform solenoidal field final focus lens with 0.5 T field for NDC region

- 3.9 T
- 0.5 T

- Envelope solution for 300 keV

- Planned experiments will be done initially with longitudinal focusing only

**Notes:**
sol4

## PIC plasma simulation in good agreement with conductivity model

- PIC
- conductivity

- PIC
- conductivity

- Beam ions superimposed

**Notes:**
Sol5, double precision

## Phase 2: 10A, 100ns He+ beam at accel end

- Compressed from 1-A 1-s beam in accel-decel injector
- 2cm, 1.2-mm-mrad, .75 J
- 60-cm long 20 kA adiabatic discharge channel
- 10-1 mm radius
- 67% energy tilt from .5-1 MeV
- Need to compress 100x and focus to 1-mm spot to achieve “HEDP” Bragg peak heating

- 750 keV He+ solution

**Notes:**
Sol42 --  used more beam than I probably have
10-ns parabolic ends

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

- Time-Integrated
- Energy Deposition

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

- Beam compresses to conditions interesting for HEDP

**Notes:**
sol42

## Detailed physics and integrated simulations of final focus design with neutralized drift compression (NDC) and discharge transport are very encouraging

- Integrated LSP simulation

## Several NDC issues addressed

- Plasma neutralization allows 50-100x drift compression with applied velocity tilt
- Two stream impact on beam small
- Filamentation minimized for rc/sd << 1, np >> nb
- Transition from Brillouin flow to NDC feasible with dipole B
- 2-stage focusing with solenoid and discharge channel transversely focuses beam with large energy tilt
- Integrated simulations of an HIF driver show good coupling to hybrid target
- NDC can be tested on proposed NTX experiment with large energy tilt, calculations show condition approaching HEDP possible  given 0.1% velocity accuracy

- Time-Integrated Energy Deposition for NTX Phase 2

- 100 ns

- 60 ns

- 140 ns

- 20 ns

- Solenoidal focusing in plasma

- Integrated driver sim.

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