Collective Focusing of a Neutralized Intense Ion Beam Propagating Along a Weak Solenodial Magnetic Field M. Dorf (LLNL) In collaboration with I. Kaganovich, E. Startsev, and R. C. Davidson (PPPL) LLNL- PRES-635456 Heavy Ion Fusion Science Virtual National Laboratory DOE Plasma Science Center, Teleseminar, DOE Plasma Science Center, Teleseminar, April 19, 2012 April 19, 2012 This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344, and by the Princeton Plasma Physics Laboratory under contract AC02-76CH- O3073
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M. Dorf (LLNL) In collaboration with I. Kaganovich , E. Startsev , and R. C. Davidson (PPPL)
Collective Focusing of a Neutralized Intense Ion Beam Propagating Along a Weak Solenodial Magnetic Field. M. Dorf (LLNL) In collaboration with I. Kaganovich , E. Startsev , and R. C. Davidson (PPPL). DOE Plasma Science Center, Teleseminar, April 19, 2012. - PowerPoint PPT Presentation
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Collective Focusing of a Neutralized Intense Ion Beam Propagating Along a
Weak Solenodial Magnetic Field
M. Dorf (LLNL)In collaboration with
I. Kaganovich, E. Startsev, and R. C. Davidson (PPPL)
LLNL- PRES-635456
Heavy Ion Fusion Science Virtual National Laboratory
DOE Plasma Science Center, Teleseminar, April 19, DOE Plasma Science Center, Teleseminar, April 19, 20122012
This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344, and
by the Princeton Plasma Physics Laboratory under contract AC02-76CH-O3073
Motivation: Controlled Fusion
2W. Sharp et al, http://hif.lbl.gov/tutorial/assets/fallback/index.html
Inertial Confinement Fusion: Lasers Versus Ion Beams
High production efficiency and repetition rate
High efficiency of energy delivery and deposition
Why ion beams?
3
Present approach – Laser Driven ICF
Promising alternative – Heavy Ion Fusion
National Ignition Facility (LLNL, Livermore, CA)
Ion-Beam-Driven High Energy Density Physics
Heavy Ion Fusion (Future) Warm Dense Matter Physics (Present)
D-T
Itotal~100 kA
τb~ 10 ns
Eb ~ 10 GeV
Atomic mass ~ 200
corresponds to the interiors of giant planets
and low-mass stars
Ib~1-10 Aτb~ 1 ns
Eb ~ 0.1-1 MeV
Ions: K+, Li+
foil Presently accessible ρ-T regime
ρ~1 g/cm3, T~0.1 ÷ 1 eV
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ion source
acceleration and transport
neutralized compression
final focusing
target
Block scheme of an ion driver for high energy density physics
ρ~1000 g/cm3
T~ 10 KeV
Neutralized Drift Compression Experiment (NDCX)
Heavy ion driver for Warm Dense Matter Experiments
5
Built and operated at the Lawrence Berkeley National Laboratory
Neutralized Drift Compression Experiment (NDCX)Schematic of the NDCX-I experimental setup
(LBNL)
Beam parameters at the target planeBeam parameters at the target plane
Weak fringe magnetic fields (~100 G) penetrate deeply into the background plasma
K+ @ 300 keV (βb=0.004)
Ib~2 A , rb < 5 mm (nb~1011 cm-3)
upgrade
NDCX-II
Li+ @ 3MeV (βb=0.03)
Ib~30 A , rb~1 mm (nb~6∙1012 cm-3)
Ttarget ~0.1 eV Ttarget ~1 eV
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8T
Fringe magnetic fields
TargetFinal Focus Solenoid
Outline
I. Enhanced self-focusing of an ion beam propagating through a background plasma along a weak (~100 G) solenodial magnetic field
Collective focusing with B0 ~ 1 kG is equivalent to standard magnetic focusing with
B0 ~10 T
important for the design of a heavy-ion driver (e.g. NDCX neutralized drift section)
II. Collective Focusing (Robertson) Lens
can be utilized in ion beam self-pinch transport applications (e.g. HIF drivers)
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neutralized ion beam
e-, i+
magnetic lens
B0
ion beam
plasma
B0
e-vb
can be used for the ion beam final focus (e.g. NDCX-I, II)
perhaps can be utilized for collimation of laser generated proton beams
I. Ion Beam Propagation through a Neutralizing Background Plasma
Along a Solenoidal Magnetic Field
ion beam
plasma
B0
e-vb
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Magnetic Self-Pinching (B0=0) The ion beam space-charge is typically well-neutralized
beam
e-
e-
e-
e-
selfB
9
t
Bself
zE Inductive field accelerates electrons
What about ion beam current?
r
z
λ=c/ωpe collisionless electron skin depth (np~1011 cm-3 → λ~1.7 cm) defines the characteristic length scale for screening current (or magnetic-field) perturbations in a cold plasma (“inductive”
analog of the Debye length)
cVBE ezselfr
1~ ebbbez nnZVV
cVBE bselfr
Electron radial force balance
Current neutralization
Magnetic pinching is dominant
jb=|je|
rb
current is well-neutralized (locally) negligible self-pinching
(b) rb>c/ωpe
jb
|je|c/ωpe
current is not-neutralized (locally) maximum (jbxBself) self-pinching
(a) rb<c/ωpe
r
Enhanced Collective Self-Focusing (B0~100 G)
There is a significant enhancement of the ion beam self-focusing effect in the presence of a weak solenoidal magnetic field (for rb<<c/ωpe)
Radial displacement of background electrons is accompanied by an azimuthal rotation Strong radial electric field is produced to balance the magnetic V×B force acting on the electrons
for
dr
dn
nVmZF b
pbebsf
122
2
2
1pe
ce
ce
bb
Vr
10
This radial electric field provides enhanced ion focusing
M. Dorf et al, PRL 103, 075003 (2009).
constrAc
ermP ee V
02B
rA
Enhanced Self-Focusing is Demonstrated in SimulationsGaussian beam: rb=0.55c/ωpe, Lb=3.4rb, β=0.05, nb=0.14np, np=1010 cm-3
Bext=300 G The enhanced focusing is provided by a strong radial self-electric field
Influence of the plasma-induced collective focusing on the ion beam dynamics inInfluence of the plasma-induced collective focusing on the ion beam dynamics in
Radial electric field
Bext=300 G LSP (PIC)
ωce/2βbωpe=9.35
NDCX-I is negligible
NDCX-II is comparable to the final focusing of an 8 T short solenoid
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e-
+ +++ +
Veφ<0
z
e-
- --- - FV×B
-eEr
Veφ>0
δr>0
z
Radial electric field is defocusing
Paramagnetic plasma response
Radial electric field is focusing
Diamagnetic plasma response
Weak magnetic field (ωce<2βbωpe)
δr<0
B0B0
Moderate magnetic field (ωce>2βbωpe)
Beam charge is overcompensated Beam charge is under-neutralized
Local Plasma Response is Drastically Different for ωce>2βbωpe and ωce<2βbωpe
resonant excitation of large-amplitude whistler waves
ωce=2βbωpe
np=1011 cm-3, βb=0.05 B0=100G
FV×B
-eEr
12M. Dorf et al, PoP 19, 056704 (2012).
Numerical Simulations Demonstrate Qualitatively Different Local Plasma