Simulations of Neutralized Final FocusD. 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

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

LSPSIMULATIONS

With plasma plugWith plasma plugand RF Plasma 100% neutralization

With plasma plugWith plasma plugand 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

(0)( ) (0) 1 v tv t vL

(0)(0)( ) (0)pp

vL v tv t v

• 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%

min L vtv v

• tmin is the minimum pulse

time for error v/v

Plasma neutralization must be excellentThe 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 = 2Ib/IA2 with Alfven current IA = mic3/eZ.

2

21 ,2 (0)rf

L ZK

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 plugand RF plasma

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 = ½ c / p , t = 1/5p 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

ballistic 4.0x1010 cm-3 1.0x1010 cm-3 2.5x109 cm-3 6.0x108 cm-3

ballistic 4.0x1010 cm-3 1.0x1010 cm-3 2.5x109 cm-3 6.0x108 cm-3

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

Two-stream impact on phase space2.5x109 cm-3 density plasma

Ballistic transport

4x1010 cm-3 density plasma

1.0x1010 cm-3 density plasma

Too low a density results in space charge spreading

Saturation of two stream growth leads to tolerable momentum spread

• 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)

Solenoidal field reduces growth rate of beam filamentation

-3000-2000-1000

010002000300040005000600070008000

0 5 10 15

Radius (cm)

Encl

osed

Cur

rent

(Am

ps)

0 kG

2 kG

8 kG

Uniform 10-cm beam

Beam matching possible from Brillouin Flow thru Neutralized Drift Compression

2 2''

2 2 2 2 3 0L Ka ac a a

Beam radius independent of energy in BF equilibrium with an energy tilt; K L

2a2/2 c2, requiring constant line-charge

With perfect neutralization, matching for NDC is energy independent

Transverse focusing in solenoid is energy dependent

with L= eB/2m, K = 2Ib /IA 2, and IA = mc3/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)

150 200 250 3001

0.5

0

0.5

1

z (cm)

Dip

ole

Fiel

d B

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+

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

4.8 kG field simulation shows no beam distortion or emittance growth

• plasma electrons are axially confined for over 110 nsLog density Beam Density 10, 80 and 150 ns

Plasma Electron Density

Small beam emittance, small variation in beam energy, constant solenoidal field strength, the entire beam can be captured within some final radius given a fractional variation in beam energy of

a0 and af 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

NDC region50-kA Discharge

Ne+

2 m 101 m

105.5 m

XXXXxxxxxxxxxxxxxxxXX

Final Focus Solenoid

2''

2 2 0La ac

0

0

8f fE E aE a

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

Log nb

100 ns

60 ns

140 ns

20 ns

Full simulation no self fields

Full simulation no self fields

Example: Ne+ ions 780 A230 MeV20% E tilt20-ns pulsea = 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

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

Plasma region

= 1012 s-1

50-kA discharge

Ne+

2 m 101 m

105.5 m

Beam couples well to hybrid target

Filamentary growth does not degrade focus

Log nb

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

(0.02C/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

4.982203.652402.132701.653002.143243.273604.22390

Energy spot

20 20 60 100 1400

1

2

ai

zi

0 50 1000

5 10 5

1 10 4

1.5 10 4

2 10 4

i

zi

3.9 T

0.5 T

Envelope solution for 300 keV

Planned experiments will be done initially with longitudinal focusing only

PIC plasma simulation in good agreement with conductivity model

PIC

conductivity

PIC

conductivity

PIC

conductivityBeam ions superimposed

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

Plasma region (1014 s-1 )

20-kA discharge

He+

0 m .92 m 1.52 m

Transition NDCSolen Focus

Adiabatic Compression

dipole trap 1.5 kG

solenoid

.72 m

1.9 T

3.5 T

0 50 1000

5 10 4

0.001

0.0015

i

zi

20 10 40 70 1000

1

2

3

ai

zi

3.5 T

1.9 T

750 keV He+ solution

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

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 nsSolenoidal focusing in plasma

Integrated driver sim.

Key unaddressed issues:Plasma must be created in varying solenoidal fieldsBeam stripping by plasma limits NDC lengthMultiple beam combining for driver