igor d. kaganovich, edward a. startsev ronald c. davidson plasma physics laboratory
DESCRIPTION
Analytical and Numerical Studies of Ion Beam Plasma Interaction for Heavy Ion Driven Inertial Fusion. Igor D. Kaganovich, Edward A. Startsev Ronald C. Davidson Plasma Physics Laboratory Princeton University. Talk Outline. Basics Why do Heavy Ion Fusion? What do we have to do? - PowerPoint PPT PresentationTRANSCRIPT
The Heavy Ion Fusion Virtual National Laboratory
Analytical and Numerical Studies Analytical and Numerical Studies of Ion Beam Plasma Interaction for of Ion Beam Plasma Interaction for Heavy Ion Driven Inertial FusionHeavy Ion Driven Inertial Fusion
Igor D. Kaganovich, Edward A. Startsev Ronald C. Davidson
Plasma Physics Laboratory
Princeton University
The Heavy Ion Fusion Virtual National Laboratory
Talk OutlineTalk Outline
BasicsWhy do Heavy Ion Fusion?
What do we have to do?
A bit about the accelerator and the beams
ProgramPast Accomplishments
Present Program
Future Plans
Physics of Ion Beam Plasma InteractionDegree of charge and current neutralization Self electric and magnetic fields
The Heavy Ion Fusion Virtual National Laboratory
Talk OutlineTalk Outline
BasicsWhy do Heavy Ion Fusion?
What do we have to do?
A bit about the accelerator and the beams
ProgramProgramPast AccomplishmentsPast Accomplishments
Present ProgramPresent Program
Future PlansFuture Plans
Physics of Physics of Ion Beam Plasma InteractionIon Beam Plasma InteractionDegree of charge and current neutralization Degree of charge and current neutralization Self electric and magnetic fieldsSelf electric and magnetic fields
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Introduction to Heavy Ion FusionIntroduction to Heavy Ion Fusion
Inertial fusion is based on H-bomb design
Who built the h-bomb? Debate revivesBy WILLIAM J. BROAD, April 24, 2001
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Heavy Ion Fusion ConceptHeavy Ion Fusion Concept
Source, Injector Accelerator
Final Focus
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How IFE Targets WorkHow IFE Targets Work
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Heavy Ion Fusion RequirementsHeavy Ion Fusion Requirements
Target requirements
3 - 7 MJ x ~ 10 ns ~ 500 Terawatts(hand grenade) (Forty times the averaged world-wide electric power
consumption)
Ion Range: 0.02 - 0.2 g/cm2 1- 10 GeV
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Peaceful Power -- An Artist’s Peaceful Power -- An Artist’s Conception of a HIF Power PlantConception of a HIF Power Plant
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Why Heavy Ion Fusion? Why Heavy Ion Fusion?
Slides of this section are courtesy of C. Celata Slides of this section are courtesy of C. Celata
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Advantages of Heavy Ion Fusion Advantages of Heavy Ion Fusion ApproachApproach• Driver is separate from the fusion chamber
accelerator not exposed to fusion environment
can protect 1st wall
• High electrical efficiency
• Takes advantage of decades of worldwide investment in accelerators & defense-funded target design
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High Energy Physics accelerators already have:
Long life
High pulse repetition rates
High efficiency (~ 30%)
Present systems comparable to requirements in:
complexitycostion energy
But: much higher charge-per-unit-length is needed. induction is not used in HEP accelerators
Heavy Ion Accelerators are a Heavy Ion Accelerators are a Good Choice for a Fusion DriverGood Choice for a Fusion Driver
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The First Wall is Protected by Neutron-The First Wall is Protected by Neutron-thick Molten Salt (FLiBe) thick Molten Salt (FLiBe) (one half cut away)
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Fusion Pocket Formed by Liquid JetsFusion Pocket Formed by Liquid Jets
Flibe (Li2BeF4), is a molten salt with twice the density of water, and roughly the same viscosity, desired for making high-pressure steam for driving turbines.
Flibe absorbs neutrons.
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Why Not Laser Drivers?Why Not Laser Drivers?
Lasers:Easy to focus
Much more money in program
Easier development path
but:Problem protecting final optics
Problem protecting first wall
Target gets damaged (hot)
Low repetition rate (a few/day)
Low electrical efficiency (a few - 10%)Glass
All
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Features of the AcceleratorFeatures of the Accelerator
3 - 7 MJ / 1- 10 GeV ions ~ 10 16 ions / 100 beams
1-2 kA / beam =>Space-charge-dominated beams (non-neutral plasma)
For accelerator design:
Focusability Multiple beams
Efficiency Induction acceleration
Stability Linear accelerator
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Talk OutlineTalk Outline
BasicsBasicsWhy do Heavy Ion Fusion?Why do Heavy Ion Fusion?
What do we have to do?What do we have to do?
A bit about the accelerator and the beamsA bit about the accelerator and the beams
ProgramPast Accomplishments
Present Program
Future Plans
Physics of Physics of Ion Beam Plasma InteractionIon Beam Plasma InteractionDegree of charge and current neutralization Degree of charge and current neutralization Self electric and magnetic fieldsSelf electric and magnetic fields
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Present ExperimentsPresent Experiments
Present experiments – higher current (larger radius)similar to the driver at low energy
high space charge potential.
0.1 - 0.5 A, 0.4 - 1 MeV, space charge potential ~ few kV
High Current Experiment (HCX) –
how much beam can be transported?
Neutralized Transport Experiment (NTX) –
neutralization by plasmas after the final focus
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The Present Experimental Program:The Present Experimental Program:HCX and NTX experimentsHCX and NTX experiments
focusing
ChamberTransport
Target
BendingLongitudinal compression
Injection Matching
MultipleBeam IonSource &Injector
Accelerationwith
electricfocusing
Accelerationwith magnetic
focusing
Many, but not all, issues experimentally explored
Very complete experimental understanding
MultibeamletInjector HCX
NTX
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The High Current Experiment HCX)The High Current Experiment HCX)
Parameters:
K+ or Cs+
~ 0.2 - 0.5 Amp
1 - 1.7 MeV
4.5 - 7 s
Quadrupoles:
10 (30-40 later) electrostatic
4 pulsed normal magnetic
a few superconducting
Issues to be resolved:
Dynamic aperture (usable aperture set by dynamics)
Halo production
Effect of desorbed gas on tail
Electron production & orbits (magnetic transport)
Mismatch, misalignment
How much beam can
be transported?
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High Current Experiment (HCX) High Current Experiment (HCX) operation since January, 2002operation since January, 2002
ESQ injector
Marx
matching
10 ES quads
diagnostics
diagnostics
Transport - aperture limits - electrons - gas effects - halo formation - steering
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Chamber Transport
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Neutralization competes with Neutralization competes with stripping in the target chamberstripping in the target chamber
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400 kV injector
Final-focusing optical system
Neutralized Transport ExperimentNeutralized Transport Experiment
FY02: characterize ion & plasma sourcesFY03: study beam aberrationsFY04: complete initial neutralization experiments
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Beam Focusing with Plasma Plug Beam Focusing with Plasma Plug ((operation since September, 2002operation since September, 2002))
Magnetic section
Pulsed arc plasma source
Drift tube Scintillating glass
WithoutPlasma
WithPlasma
Beam simulations and theory span a variety Beam simulations and theory span a variety of processesof processes
two-stream instability
acceleration in 3-D structure
beam ions Flibe ions electrons
target
chamber propagation electrons during neutralization
halo generationx
px
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Integrated Beam eXperiment Short-Pulse Integrated Beam eXperiment Short-Pulse Source-to-Focus ExperimentSource-to-Focus Experiment
Drift Compression/Bend section
Shaping/matchingsection
Injector
2 m250 ns
Accelerator
40 m
Velocity tilt section
FinalFocus
vsect
7m25 ns
15 m, 10 MeVCompress x
250 25 ns 1
10
Ion: K+
1 beamline
Pulse duration: 250 ns -> 25 ns
Final energy: 5 - 10 MeV
Total half-lattice periods: 148
Total length: 64 m
Cost: ~ 70 M$
$50 - 70 M TEC over 5 yrs + $15 M R&D
1.7 MeV 10 MeV
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Heavy Ion Fusion SummaryHeavy Ion Fusion Summary
• Because of the separation of accelerator from fusion chamber, the heavy ion fusion concept is able to protect the 1st wall, and the driver, from fusion products.
• HIF benefits from large U.S. and worldwide investments in accelerators and defense-funded target research.
• Past and present experiments have demonstrated production, acceleration, compression, and focusing of beams at lower energy and current.
• The Integrated Beam Experiment would be a proof-of-principle experiment with a rich physics mission: to explore longitudinal physics and test integrated source-to-focus transport.
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Talk OutlineTalk Outline
BasicsBasicsWhy do Heavy Ion Fusion?Why do Heavy Ion Fusion?
What do we have to do?What do we have to do?
A bit about the accelerator and the beamsA bit about the accelerator and the beams
ProgramProgramPast AccomplishmentsPast Accomplishments
Present ProgramPresent Program
Future PlansFuture Plans
Physics of Ion Beam Plasma InteractionDegree of charge and current neutralization Self electric and magnetic fields
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Means of InvestigationMeans of Investigation
Nonlinear theoryNumerical simulation:
– Particle in cell– Fluid
Neutralization experiment (VNL)
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Results of 2D PIC-MC CodeResults of 2D PIC-MC Code
•Beam propagation in the y-direction, •beam length 7.5 c/p;
•beam radius 1.5 c/ p; •beam density equal to the half of the plasma density; •beam velocity c/2.
•Shown are electron density and the current.
The Heavy Ion Fusion Virtual National Laboratory
The Heavy Ion Fusion Virtual National Laboratory
beam length 30. c/p;
beam radius 0.5 c/ p; •beam density is 5 of plasma density; •beam velocity 0.5c.
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System of EquationsSystem of Equations
0,ee e
nn V
t
1( ) ( ),e
e e e
p eV p E V B
t m c
4 1,b b bz e ez
e EB Z n V n V
c c t
1.
BE
c t
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Steady- State Results (current flow)Steady- State Results (current flow)
FOR MORE INFO...
http://hifnews.lbl.gov/hifweb08.html
Beam propagates in the y-direction, beam half length lb=15 c/ p ;
beam radius rb =1.5 c/ p ;
beam density nb is equal to the background plasma density np; beam velocity Vb=c/2.
Shown are the normalized electron density ne/np and the vector fields for the current.
Dir
ecti
onD
irec
tion
of p
ropa
gati
on o
f pro
paga
tion
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Steady- State Results (electric field)Steady- State Results (electric field)
FOR MORE INFO...
http://hifnews.lbl.gov/hifweb08.html
Beam propagates in the y-direction, lb=15 c/ p ;
rb =1.5c/ p ;
nb = np; Vb=c/2.
Shown are the normalized electron density ne/np and the vector fields for the electric force on electrons. D
irec
tion
Dir
ecti
on o
f pro
paga
tion
of p
ropa
gati
on
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Steady- State ResultsSteady- State Results
http://www.trilobites.comnormalized electron current jy/(ecnp)
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Analytic theory of chamber transport: excitation of Analytic theory of chamber transport: excitation of plasma waves by beam depends on bunch lengthplasma waves by beam depends on bunch length
b=0.5, lb/rb =10, nb/np=0.5 a) lb= 2Vb/p , b) lb= 6Vb/p , c) lb= 20Vb/p .
Red line: ion beam size, brown lines: electron trajectory in beam frame
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Nonlinear TheoryNonlinear Theory
Important issues:– Finite length of the beam pulse,– Arbitrary value of nb/np (nb>>np),– 2D.
Approximations:– Fluid approach, – Conservation of generalized vorticity,– Long dense beams lb >> rb , Vb/p.
Exact analytical solution.
If you would like to experience delicious taste, bite in small pieces.
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Conservation of Generalized Conservation of Generalized VorticityVorticity
( ) 0,ee eV
t
/ ,e ep eB c
( ) .,e e
edS p A r const
c
0 / .e ep eB c
FOR MORE INFO... I. Kaganovich, et.al, Physics of Plasmas 8, 4180 (2001).
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Approximate System of EquationsApproximate System of Equations
lb >> rb,
,e
e
c p B
1( ) 0,e
ey b e er
nV V rn V
y r r
14 ( ),r b b p eE e Z n n n
r r
( ) ,er eey b r
p KV V eE
y r
1 4.ey b b by e ey
er p Z n V n V
r r r c
2 / 2,e e eK m V
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Simplified CodeSimplified Code
Approximation of long beams:– Beam length is much longer than beam radius;
– Therefore, beam can be described by a number of weakly interacting slices.
– The electric field is found from radial Poisson’s equation.
– As a result of the simplification the second code is hundreds times faster than the first one and can be used for most cases, while the first code provides benchmarking for the second.
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Comparison of Theory and Comparison of Theory and Simulation: Electron DensitySimulation: Electron Density
Electron densityLeft – PIC, Right - fluid
lb =1c/ p, rb =0.1c/ p nb=0.5np , Vb=0.5c
Brown lines: electron trajectory in the beam frame.
Red line: ion beam size.
FOR MORE INFO...I. Kaganovich et.al, http://pacwebserver.fnal.gov/papers/Tuesday/PM_Poster/TPPH317.pdf
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Comparison of Theory and Comparison of Theory and Simulation: Electron DensitySimulation: Electron Density
Key parameter p lb/Vb,
Quasineutrality lb>>Vb / p.
lb =30c/ p
rb =1.5c/ p
np=nb
Vb=0.5c
-4 -2 0 2 4
0
2 (a) ne
nb
y=25c/p
y=0
n e/np, n
b/np
xp/c
0.10
0.10
1.0
-4 -2 0 2 4
-30
-20
-10
0
10
20
30
y=0
Ion Bunch Density
y=25c/p
yp/c
xp/c
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Comparison of Theory and Comparison of Theory and Simulation: Current NeutralizationSimulation: Current Neutralization
Key parameter prb/c,
Current neutralization rb>>c /p.
lb =30c/ p
rb =1.5c/ p
np=nb
Vb=0.5c
-4 -2 0 2 4
-0.1
0.0
0.1
0.2
0.3(b) y=25c/
p
y=0
PIC Fluid
j y/(en
pc)
xp/c
0.10
0.10
1.0
-4 -2 0 2 4
-30
-20
-10
0
10
20
30
y=0
Ion Bunch Density
y=25c/p
yp/c
xp/c
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Comparison of Theory and Comparison of Theory and Simulation: Magnetic FieldSimulation: Magnetic Field
FOR MORE INFO... I. Kaganovich, et.al, Physics of Plasmas 8, 4180 (2001).
Key parameter prb/c,
Magnetic field neutralization rb>>c /p.
lb =30c/ p
rb =1.5c/ p
np=nb
Vb=0.5c
-6 -4 -2 0 2 4 6-0.1
0.0
0.1
z=25c/p
z=0(c)
PIC Fluid
eB/(
2wpm
ec)
xp/c
0.10
0.10
1.0
-4 -2 0 2 4
-30
-20
-10
0
10
20
30
y=0
Ion Bunch Density
y=25c/p
yp/c
xp/c
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Results and ConclusionsResults and Conclusions
Developed a nonlinear fluid theory for the quasi-steady-state propagation of an intense ion beam pulse in a background plasma under the assumption of a long beams lb>>rb.
– The analytical formulas can provide an important benchmark for numerical codes.
– The analytical solutions form the basis of a hybrid semi-analytical approach, used for calculations of beam propagation in the target chamber.
The simulations of current and charge neutralization performed for conditions relevant to heavy ion fusion showed:
– very good charge neutralization: key parameter p lb/Vb,
– very good current neutralization: key parameter prb/c.
Plasma wave breaking heats electrons nb >np.
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Results of 2D PIC-MC CodeResults of 2D PIC-MC Code
•Beam propagation in the y-direction, •beam half length 7.5 c/p;
•beam radius 1.5 c/ p; •beam density equal to the half of the plasma; density; •beam velocity c/2.
•Shown is the electron current.
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The Heavy Ion Fusion Virtual National Laboratory
Plasma Wave Breaking Heats the Electrons when nb >np
Electron phase space shown for lb=30Vb/p; nb = 2np .
Times after entering the plasma plug are: (a) 113 /p , and (b) 245/p .
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Fluid approximation is good for Fluid approximation is good for nb np
Electron current and phase space lb=15c/p; nb = np ; Vb =c/2.
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Results of 2D PIC-MC CodeResults of 2D PIC-MC Code
•Beam propagation in the y-direction, •beam half length 30 c/p;
•beam radius 0.5 c/ p; •beam density is equal to 5 of the plasma density; •beam velocity c/2.
•Shown is the electron density.
The Heavy Ion Fusion Virtual National Laboratory