modeling of intense ion beam transport and focusing for high … · 2016. 6. 24. ·...
TRANSCRIPT
Presented for LBNL Center for Beam Physics
11/29/2012
Mikhail Dorf
Lawrence Livermore National Laboratory, Livermore, CA 94550
Heavy Ion Fusion Science
Virtual National Laboratory
Modeling of Intense Ion Beam Transport and
Focusing for High Energy Density Physics Applications
In collaboration with
PPPL: R. Davidson, I. Kaganovich, E. Startsev, H. Qin, E. Gilson
LLNL/LBNL : A. Friedman, R. Cohen, D. Grote, S. Lund, P. Seidl, S. Lidia, J. Barnard, J. Kwan
IAP RAS (Russia): V. Zorin, A. Sidorov, V. Skalyga, and the ECR team
LLNL-PRES-605078
This research was supported by USDOE contracts DE-AC52-07NA27344 and AC02-76CH-O3073; Russian Foundation for Basic Research (RFBR), grant n0.
11-02-97056-r_povolzhie_a; Federal Targeted Program "Scientific and Educational Personnel of the Innovative Russia" for 2009-2013;
Ion-Beam-Driven High Energy Density Physics
High production efficiency and repetition rate
Heavy Ion Fusion (Future) Warm Dense Matter Physics (Present)
High efficiency of energy delivery and deposition
Why ion beams?
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 A
τb~ 1 ns
Eb ~ 0.1-1 MeV
Ions: K+, Li+
foil Presently accessible ρ-T
regime
ρ~1 g/cm3, T~1 eV
2
Outline
Modeling of gas-dynamic ECR plasma ion source
Studies of nonlinear dynamics and collective processes in intense
ion beams in periodic focusing accelerators and transport systems
ion
source
acceleration
and transport
neutralized
compression
final
focusing
target
Studies of neutralized ion beam transport along a weak
solenoidal magnetic field
Studies of collective ion beam focusing by a weak solenoidal
magnetic field
This presentation reviews studies of transport properties of an
intense ion beam propagating in an ion driver
3
Ion driver
• Ion beam extraction
• Emittance measurements
• Equilibrium (matched) beam distributions
• Halo production by a beam mismatch
• Enhanced self-focusing
• Electromagnetic wave excitation
• Collective focusing magnetic lens
• Collective focusing for NDCX final focus
Neutralized Drift Compression Experiment (NDCX)
Beam parameters at the target plane
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
4
8T
Target Final Focus
Solenoid
Schematic of the NDCX-I experimental setup (LBNL) The heavy ion driver for Warm Dense Matter Experiments
I. Modeling of the ion beam extraction from a gas-
dynamic ECR plasma ion source
5 5
30kV 0 kV
Pla
sm
a
Ion beam
R-Z PIC (WARP) simulations
R (m)
Z (m)
References
[1] M. Dorf et al., J. Appl. Phys. 102, 054504 (2007).
[2] M. Dorf et al., Phys. Plasmas, 15, 093501 (2008).
[3] M. Dorf et al., submitted to Nucl. Instr. Meth. Res. A (2012).
[4] A. Sidorov, M. Dorf, et al., Rev. Sci. Instrum. 79, 02A317 (2008).
Gas-Dynamic ECR Ion Source (SMIS 37)
6
Extracted beam
I~150 mA
εN~0.9 π∙mm∙mrad
j~1A/cm2
N+ N++ N+++
<Zi>~2
ECR dischargebeam
Puller
FC
L~30 cm
Magnetic
trap (2T)
Lp~25 cm
Plasma electrode
(U~20-60 kV)
Microwave
radiation
(37.5 GHz,
100 kW)
n~1013 cm-3 Te~50 eV
6
High current / Low Charge State
ion sources
Multi-charged / Low current ion
sources
Gas-dynamic ECR ion source
Vacuum arc sources (MEVVA), RF (multicusp) ECR ion sources (classical) Zi >> 1
Moderate charge-state (Zi>1) High beam current
SMIS 37
Build and operated
IAP RAS (Russia)
Gas-dynamic ECR source looks promising as a source for HIF driver
7
Principles of the Ion Beam Extraction from Plasma
i
eeff
effBM
TZenZj 061.0
Bohm current Child-Langmuir current
2
0
2/3
72.1d
U
A
Zj
i
eff
CL
d0
Plasma-vacuum surface (meniscus) evolves in order to match jB ≈ jCL
S0 0
Uext U=0
7
d>d0
S>S0
S<S0
d<d0
Low-density plasma (jB<j0CL) Overdense plasma (jB>j0CL)
WARP code WARP code
jb / jCL ≈ 0.5 jb / jCL ≈ 9
Single-aperture extraction: Experiment and Simulations
Experiment WARP code
0
0.5
1
1.5
2
2.5
3
3.5
15 25 35 45 55
IFC (mA)
U (kV)
d0=3 mm
d0=7 mm
np0=2.4×1012 cm-3, Ti=10 eV
np0=2.8×1012 cm-3, Ti=10 eV
8
φp+U
φp+U
φp+
U
U
U
N+ N2+ N3+
0 V
0 V
Boltzman
Electrons
Vs
Extracting
electrode (puller)
Secondary
electrons
(not included in
the simulations)ion
Fara
day C
up
IFC
IPe-
Schematic of WARP simulations Extracted beam current
The results of the numerical simulations are in very good agreement
with the experimental measurements
Plasma sheath model
• Ions are injected with the Bohm velocity
• Boltzman electrons with Te= 50 eV are assumed
• Possion equation is used for potential variations
• N+:N++:N+++ obtained from measurments
• np0 and Ti are chosen to match the measurements
Extraction aperture - 1 mm
d0
M. Dorf et al. submitted to NIMA (2012)
Noise Suppression and Stabilization of an Ion Beam
Extracted from Overdense Plasma
Beam formation in the plateau regime
significantly enhances the brightness (BPlateau~16Bregime of maximum extracted current)
provides stable extraction despite large plasma fluctuations
9
0.0
0.4
0.8
1.2
1.6
2.0
0.0 0.2 0.4 0.6 0.8
Plasma density, 1013cm-3
IFC (mA)
Large fluctuations
Larg
e n
ois
eLarge fluctuations
Low
nois
e
Plateau
WARP Simulations
0
0.4
0.8
1.2
1.6
2
0 200 400 600 800 1000 1200
Jpuller+JBCF, mA/cm2
IFC (mA)Experimental dataIllustrative cartoon
M. Dorf et al., J. Appl. Phys., 102, 054504 (2007).
It is of particular practical importance to suppress noise in the extracted
beam current provided by fluctuations in the plasma density
Measurements of the Transverse Beam Emittance
Images of
plasma
discharge
Scintillator plate image Beam phase-space measurements
using the pepper-pot method
Beam phase-space reconstruction
Multiaperture plasma electrode
2 cm
Ø=3mm
The diagnostics demonstrates high values of the ion beam transverse temperature (~10 eV)
A. Sidorov, M. Dorf, V. Zorin, et al.,
Rev. Sci. Instrum. 79, 02A317 (2008).
Schematic of the diagnostics setup
10 10
Similar assumption of high ion temperature (~10 eV) was required in numerical modeling to match the experiments
A reduced analytical model was developed to explain such high ion temperatures M. Dorf et al, Phys. Plasmas, 15, 093501 (2008).
II. Studies of nonlinear transverse beam dynamics in
periodic focusing transport systems
11 11
References
[1] M. Dorf et al., Phys. Plasmas, 18, 043109 (2011).
[2] M. Dorf et al., Phys. Plasmas, 16, 123107 (2009).
[3] M. Dorf et al., Phys. Rev. ST AB 9, 034202 (2006).
[4] M. Dorf et al., PAC Proceeding 2007; 2009.
Periodic Focusing Lattices
ˆ ˆ( ) ( )( )
ˆ ˆ( ) ( )( )
q q x y
foc
q q x y
B x B z y x
F x z xe ye
e e
Alternating-gradient quadrupole lattice Periodic-focusing solenoidal lattice
z
Smooth-focusing approximation
Single-particle motion (no space-charge forces)
rsffoc rF e
1ˆ ˆ ˆ( ) ( )( ) ( )
2
ˆ ˆ( ) ( )( )
sol z x y z z
foc
sol s x y
B x B z y x B z
F x z xe ye
e e e
12
SSmooth focusing
(betatron) period,
2π/κsf
Vacuum phase advance
σvac = κsfS/2π
In the presence of space charge, the phase advance, σ, is depressed,
σ<σvac
σ/σvac→1 emittance dominated beam
σ/σvac→0 space-charge dominated beam
z
x
Equilibrium (Matched) Beam Distribution
Smooth-focusing approximation
ˆ ˆfoc
sf sf x yF x y e e
Beam Equilibrium
The transverse Hamiltonian
(particle energy) is not conserved The transverse Hamiltonian is an
invariant of beam particles motion
Oscillating focusing field
0 2 2 21 1
2 2sfH x y r r
Kinetic
energy
Applied focusing
potential
Self-
potential
000
Hff bb
Equilibrium (matched) beam envelope
Szz latticelattice
How to find (or load) a matched-beam quasi-equilibrium?
Quadrupole lattice
X, Y beam
envelope
z
S
Szfzf bb
z
Rb
Matched beam
envelope
Nonlinear effects of the intense
beam self-fields provide a significant
challenge for analytical studies
1
3
ydxdfr b
13
Adiabatic Formation of a Matched Beam Distribution
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 10 20 30 40 50 60
0
rms
b
X
X
Evolution of the beam envelope
σ/σvac=0.26, σvac=660
s/S
2 1 q
q sf x y q x yF V s x y V s s x y e e e e
Smooth- focusing
equilibrium with Quasiequilibirum
matched to a
quadrupole lattice
Adiabatic turn-off of the
uniform focusing field Adiabatic turn-on of the
oscillating focusing field
The average (smooth-focusing) effects of the total
focusing field is maintained fixed
Quiescent beam propagation over several hundred lattice periods has been
demonstrated for a broad range of beam intensities and vacuum phase advances
V(s)
s
1
0
Transition function
Quadrupole lattice (WARP simulations)
Dorf et al., Phys. Plasmas 16, 123107 (2009) 1
4
THfb
0exp
FFT of the beam envelope time evolution
Mismatch
modes
~6 orders of magnitude
14
Self-Similar Beam Density Evolution
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.0 1.5 2.0 2.5
Quadrupole lattice σ/σvac=0.26, σvac=660 (WARP simulations)
0bx R
( )x a s
Regularly normalized coordinates
Scaled coordinates
-1.0
-0.5
0.0
0.5
1.0
1.5
56 57 58 59 60
Self-similar beam density evolution has been demonstrated for a broad range of
beam intensities. The self-similarity feature becomes less accurate for σvac~800. Dorf et al., Phys. Plasmas 16, 123107 (2009)
0
2
0
)()(
b
b
bn
n
R
sbsa
Beam
density
0b
b
n
n
Beam
density
Evolution of the beam envelope
0
rms
b
X
X
Lattice
function
Number of periods
κq(s)
sXsa rms2
sYsb rms2
Contour plots of the beam density (σvac=450)
1
5 15
ω1
ω2
Due to the nonlinear effects of
the beam self-fields particles
with higher energy move with
higher frequency
Rb
z
Matched
beam radius
Mismatch
oscillations
ωpart~ ωmis/2
Parametric resonant
interaction
Smooth-focusing approximation
Halo Production by a Beam Mismatch
Resonance
(O point)
Separatrix X point
R
VR
Radial Phase Space
core
halo
Energy transfer Collective motion Individual motion
(each particle is an oscillator)
Beam Halo
Cause degradation of the beam quality
Can provide activation of the chamber wall
One of the important problems:
How to quantitatively define
beam halo?
16
16
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
-5
-4
-3
-2
-1
0
1
2
3
4
5
0 1 2 3 4 5
Spectral Method for Halo Particle Definition
Bump-on-tail structure for ωβ>ωm/2 can be
attributed to beam halo particles
Smooth-focusing model (WARP simulations)
Beam is an ensemble of betatron oscillators
Initial
(matched)
distribution
Final
(mismatched)
distribution
Snapshot
Poincare plots
Radial phase-space
core halo
halo
halo core
FFT of a particle trajectory
Betatron
frequency
distribution
(a.u.)
R
R
R
R
qx
qx
25.0vac ωm/2
halo
Consider a mismatched intense beam with δRb/Rb=0.12
ωq=κsfVb smooth-focusing frequency
ωm frequency of mismatch oscillations
Beam
frame
17 17
M. Dorf et al Phys. Plasmas, 18, 043109 (2011).
Extension of the Spectral Method to the Case of a
Quadrupole Lattice
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
Quadrupole lattice (WARP simulations)
Betatron
frequency
distribution
(a.u.)
qx
X
X
X
X
25.0vac
Bump-on-tail structure for ωβ>ωodd/2 can be
attributed to beam halo particles
ωodd/2 ωeven/2
Symmetric (even) and quadrupole (odd)
modes are simultaneously excited
halo
initial (matched)
final
(mismatched)
Transverse phase-space
Halo
removal
18 18 M. Dorf et al Phys. Plasmas, 18, 043109 (2011).
017vac
0,0
0,2
0,4
0,6
0,8
1,0
1,2
0,0 0,2 0,4 0,6 0,8 1,0
Smooth-focusing approximation. Intense beam with σ/σvac=0.25 (WARP simulations)
We introduce a mismatch by an instantaneous increase in the smooth-focusing frequency
ωqf=1.4ωqi
Beam betatron frequency distribution
ω/ωqf
1.0
1.2
1.4
1.6
1.8
2.0
0 1000 2000 3000
Normalized emittance
ωm/2
ωqi t/2π
Most of the halo is generated relatively fast
Core relaxation process takes much more time
Core relaxation process also leads to emittace growth
Emittance after the
halo removal
Frequency distribution @ t=617*2π/ωqi
t=3140*2π/ωqi
f
i
Nu
mb
er o
f p
arti
cles
(ar
bit
rary
un
its)
Mismatch Relaxation in Intense Beams
19 19
III. Intense Ion Beam Transport through a
Background Plasma
Weak fringe magnetic fields (~100 G) penetrate deep into background plasma.
Can a weak solenoidal magnetic field has a significant influence on intense ion
propagation through a background plasma?
20 20
8T
Fringe magnetic fields
Target Final Focus
Solenoid
Schematic of the NDCX-I experiment
III. Ion Beam Propagation through a
Neutralizing Background Plasma Along a Solenoidal Magnetic Field
ion beam
plasma
B0
e- vb
21 21
References
[1] M. Dorf et al., Phys. Plasmas, 19, 056704 (2012) .
[2] M. Dorf et al., Phys. Plasmas, 17, 023103 (2010).
[3] M. Dorf et al., Phys. Rev. Lett., 103, 075003 (2009).
Enhanced Self-Focusing of an Intense Ion Beam Pulse
22
Weak magnetic field is applied Magnetic field is not applied
B0=0 B0~100 G
The ion beam space-charge is typically better compensated than the beam current
There is a significant enhancement of the ion beam self-focusing
effect in the presence of a weak solenoidal magnetic field.
e-
fM
fE
Veφ>0
δr>0
z
ωce>> ωpeβb
B0 beam
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 Net self-pinching force is produced due to the self-magnetic field
The total self-focusing force is given by
M. Dorf et al., PRL 103, 075003 (2009)
for
The effects of self-pinching is maximum for rb<<c/ωpe, and the focusing force is given by
pe
b
pe
ce
ce
b cr
V
2
2
1
drrnrn
Vmc
ZF b
p
be
pe
bsp
12
2
2
2
dr
dn
nVmZF b
p
bebsf
122
Fsf/Fsp~(c/ωperb)2>>1
zbeam
e- e-
e- e-
Self-pinching effect
selfB
22
Enhanced Self-Focusing is Demonstrated in Simulations
Gaussian beam: rb=0.55c/ωpe, Lb=3.4rb, β=0.05, nb=0.14np, np=1010 cm-3
-60
-40
-20
0
20
40
60
0 2 4 6 8
Central
beam
slice
Beam density profile
Analytic
LSP (PIC)
R (cm)
Bext=0
Magnetic self-pinching Collective self-focusing
Fr/Zbe
(V/cm)
Radial focusing force
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 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
M. Dorf et al, PRL 103, 075003 (2009). 23
Electromagnetic Wave Excitation
PIC (LSP) Semi-analytic Analytic
Magnetic pick-up loop Numerical integration (FFT)
assuming weak dissipation
Analytical treatment of poles in
the complex plane
Analytic theory is in very good
agreement with the PIC simulations
Wave-field excitations can be used for
diagnostic purposes
Strong wave excitation occurs at
ωce/2βbωpe (supported by PIC simulations)
βb=0.33, lb=10rb, rb=0.9∙c/ωpe, nb=0.05np, Bext=1600G, np=2.4∙1011cm-3
Transverse magnetic field (Whistler waves)
M. Dorf et al, Phys. Plasmas, 17, 023103 (2010).
IV. Collective Focusing Lens for Final Beam Focusing
25
Schematic of the present NDCX-I final focus section
drift section
(8 Tesla)
FFS
25
Challenges:
Can a weak magnetic lens be used for tight final beam focusing?
Operate 8 T final focus solenoid
Fill 8 T solenoid with a background plasma
neutralized ion beam
e-, i+
magnetic lens
B0
IV. Collective Focusing of an Intense Neutralized Ion Beam Pulse
26 26
References
[1] M. Dorf et al., Phys. Plasmas, 18, 033106 (2011).
[2] M. Dorf et al., PAC Proceeding 2011.
Collective Focusing Lens Collective Focusing Concept (S. Robertson 1982, R. Kraft 1987)
27
Strong ambipolar electric field is produced to balance the magnetic V×B force
acting on the co-moving electrons
Centrifugal
force
V×B magnetic
force
Electric
force
The use of a collective focusing lens allows for decrease in the magnetic field by (mi/me)1/2
Conditions for collective focusing
r
VmBV
c
eeE
e
eer
2
0
2
rV cee From conservation of
canonical angular momentum
e
rmE eer
4
2The radial electric field is
given by
To maintain quasi-neutrality 2pe e
To assure small magnetic field
perturbations (due to the beam)
peb cr 2
27
e i+ei
Le ~0.01 mm Li ~ 10 m Lc=(LeLi)1/2 ~ 1 cm
B=500 G
L=10 cm
Electron beam
focusing
Ion beam
focusing
Neutralized
beam focusing
B=500 G
L=10 cm
B=500 G
L=10 cm
β=0.01 β=0.01 β=0.01
The collective focusing concept can be utilized for final ion beam focusing in NDCX.
No need to fill the final focus solenoid (FFS) with a neutralizing plasma
Magnetic field of the FFS can be decreased from 8 T to ~700 G
Collective Focusing Lens for a Heavy Ion Driver Final Focus
Schematic of the present NDCX-I final focus section
Beam can drag neutralizing electrons from the drift section filled with plasma.
drift section
(FFS)
28
FFS
28
Numerical Simulations Demonstrate Tight Collective Final Focus for NDCX-I
Schematic of the NDCX-I simulation R-Z PIC (LSP) Beam injection parameters:
K+ @ 320 keV, rb=1.6 cm,
Ib=27 mA Tb=0.094 eV,
Plasma parameters
(for the simulation II)
29
-10
-8
-6
-4
-2
0
2
4
0 0.4 0.8 1.2r (cm)
Er (k
V/c
m)
Radial electric field
inside the solenoid
Analytic
LSP (PIC)
35 266 271 281
Plasma
Final Focus Solenoid
(700 G)
2 c
m
beam
Conductivity
model
kin
etic
251
Tilt gap
z=8 -11
0
I simulation II simulation
z (cm)
np=1011 cm-3, Te=3 eV
M. Dorf et al., Phys. Plasmas, 18, 033106 (2011).
280 281 282 283 0
0.05
0.1
0.15
0.2
z (cm)
r (c
m)
nb (cm-3)
(a)
Beam density
@ focal plane
6×1012 cm-3
29
Conclusions
30
acceleration
and transport
neutralized
compression
final
focusing
• A numerical method for the adiabatic formation of a
quasi-equilibrium beam distribution matched to a
periodic focusing lattice was developed
• A spectral method for beam halo definition was proposed
• Enhanced self-focusing of an intense ion beam pulse
propagating through a magnetized plasma background
was found
• The feasibility of tight collective focusing of intense ion
beams for NDCX was demonstrated
Transport properties of intense ion beam pulse propagating in an ion
driver have been investigated, in particular:
30
ion
source
• Electromagnetic (whistler) wave excitation was analyzed
• Modeling of the ion beam extraction from the SMIS-37
ion source was performed
• Low-noise extraction regimes were identified
• Ion beam transverse emittance was analyzed