yakov krasik physics department, technion pulsed power plasma cathodes for relativistic high-current...
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Yakov Krasik
Physics Department, Technion
• Pulsed Power
• Plasma cathodes for relativistic high-current electron beams
• Microwave generation
• Underwater electrical wire explosion
• Generation of converging strong shock waves
Pulsed-Power Plasma and its Applications
What is Pulsed Power ?
Power 109-1014W, Energy 105-107eV Current 104-107A, Pulse duration 10-9-10-5 s
• Slow storage of energy (100-2 s)
• Compression stages (10-6 - 10-7 s)
• Forming and Transmission Elements (10-8 s)
• Load: electron and ion diodes, z-pinches, antenna
• Product: pulsed power discharges, beams of charged particles, X-rays, neutron bursts, plasma heating, microwaves, laser beams, magnetic field compression.
Pulsed Power Applications
• Strong Shock Wave Generation (electron and ion beams)
Pressure ~ Pb /(S); Pb ~ 1013 W/cm2 Pressure ~ 10Mbar
• High-Power Microwaves (Microwave power 10 GW)
• Thin Film Preparation
• High Intensity Neutron Fluxes ( Ion beam 1013 1n0/pulse)
• High-Power Pulsed Gaseous Lasers
• Strengthening and Modification of Materials
• High-Power Bremsstrahlung Sources (Electron beams)
Dose ~ Ee2.8Ie (HERMES III: 20MeV, 700kA, 30ns 100 kRad at 500 cm2)
כור היתוך (ריאקציה מיזוג גרעיני)
MeV .5971Qn HeHH
MeV 03.4Q HHeHH
MeV 3.27Qn HeHH
106.52
3
14.0)(
10
42
31
21
11
31
21
21
10
32
21
21
08
221
KTTkU
MeVR
ek
R
qqkU
B
ee
דאיטריום טריטיום
Confinement Fusion
2
14 3 15 3
3[ ] 12
[ / ] 0.25 (3.6 )
At = 25 keV min 1.5 10 / 10 s keV/cm
eE e E
loss e DT DT DT DT
e E e EDT
kTnW J kTn
P J s n V E V E MeV
TT n s cm n T
V
VnVnnf DTeDTTD 225.0
2H1 +3H1 4He2 (3.6 MeV)+1n0 (14 MeV) [Energy: 1 kg 1014 J]
Confinement time
The volume rate of fusion reactions: ( )DT lossfE P
International Thermonuclear (Tokamak) Experimental Reactor: ITER [2015 (2021)]
n 1014 cm-3; T 10 keV; 400 s; Pin = 40
MW;
Pout = 500 MW (0.5 g D-T in 840 m3 volume)Plasma major radius: 6.2 m; Plasma minor radius: 2 m
Plasma current – 15 MA; Average neutron flux: 0.5 MW/m2
Magnetic field at axis: 5.3 T
Toroidal magnetic field energy – 41010 J
Inertial Confinement Fusion
14 3 1.5 10 / e En s cm iE MkTR //
• Electron Beams• Ion Beams
Confinement time: time it takes sound waves to travel across the plasma
21 /R g cm
Solid DT: 0.2g/cm3. Compression:104. R=0.1mm. Pressure:106bar. Energy: 106J. Power:1014W/cm2
Electron/Ion/Laser beams or soft x-rays
rapidly heat the surface ofthe fusion target forming asurrounding plasma layer
CompressionTarget is compressedby plasma expansion
Ignition The fuel core reaches 104 of T-D densityand ignites at 10 keV
Burn Thermonuclear burn spreads through the compressed T-D, yielding the input energy.
• Laser Beams (NIF: Lawrence Livermore National Lab)• Soft X-rays (Z-pinch: Sandia National Lab)
Adiabatic compression: 3
1RnConst
T
PV
ConstVT
ConstVP
Z-pinchUSA, UK, France, Russia, Israel, Japan, China
2
/ 2
11 MJE
Electric field
energy
W CU 2
/ 2
20MA 150 nsM
Magnetic field
energy
W LI2
7
/ 2
7.5 10 /
K i i
Kinetic energy
W NM V
V cm s
T
Thermal energy
W NkT
Soft X-ray radiation2 MJ, 290 TW
Hohlraum radiation temperature 200 eV
40mm Tungsten wire Array 240 5m wires
Sandia National Laboratory
Z-pinch (Z-accelerator: upgrade to 60 MA) Achieved: X-ray output: 1.9 MJ, 280 TW
Achieved: conversion efficiency: 15% Required X-ray output: 10MJ,1000TW
D-T target energy: 1000 MJ
M. G. Haines, et al. Phys. Plasmas 7, 1672 (2000)
Z-accelerator
High-current electron beams
EA = EC Qi=Qe Iete = Iiti Ie = Ii(mi/me)1/2
2
2/32/1
,,
2/12/1
,,
,
,
)()(
9
2
2
444
tVdm
eSI
e
mj
V
j
plieie
ieie
ie
ie
Planar diode
• Alfven current: IA = 17 [kA]
• Space-charge-limited current: Is-ch= (mec3/2e)(2/3 - 1)3/2/[1+2ln(R/rb)]
• Lawson current: IL = IA2(2+ f - 1)-1, f = (ni/ne)
High-current electron diodeExample of closure of Anode-Cathode gap by plasma
dac= 20mm, Ua= 180 kV, I = 2.5 kA. Frame 10 ns
0 1 2 3 4 50.0
0.2
0.4
0.6
0.8
1.0 80 ns 180 ns 280 ns
Rel
ativ
e po
tent
ial
Distance from the anode (cm)
Potential distribution in the plasma prefilled diode
High current ion beams
Reflex systems
Planar bipolar diode: Ii = Ie(me/Mi)1/2
It is necessary to increase life-time of electrons in the anode-cathode gap
Magnetically insulated ion diode
PFBA II: Li-ion beam: Ei = 6MeV, Ii =1MA, t=25ns, W =1.4TW/cm2
Necessary for ignition - 5 TW/cm2
Explosive Emission PlasmaThe maximum current density which can be emitted from the explosive plasma is restricted by self-space charge
E A/d; E r-2
Drawbacks of explosive emission plasma
Fast plasma expansion velocity.
Time delay of the plasma appearance.
Plasma non-uniformity.
Flashover Plasma
00
1)( fe
ACf
m jl
dl
dtd
Carbon fiber cathode Formation of emission centers depends strongly on the growth rate of the electric field
Flashover Plasma (ferroelectric plasma cathodes)
Polarization Reversal model Plasma model
Light Emission (BaTiO3 cathode, )
Frame 5 ns
Plasma Opening Switch
0
200
400
Ele
ctro
n be
am
curr
ent [
kA]
P
OS
curr
ent [
kA]
Time [ns]
POS
volta
ge
[k
V]
0
20
40
0 200 400 600 800 1000 1200
0
10
20
• Anomalous fast magnetic field penetration
Classical diffusion time:s
c
L 462
21010
4
Experiment: 10-8 - 10-6 s
• Fast increase of the plasma resistivity: 107-109 s
• Generation of high-current electron and ion beams
• Electron Magnetohydrodynamics (Hall
effect )
•
BBB
B )4/(])(
[)4/(/ 2 cn
ecte
scmnr
re
cBV rc /1010)
1(
487
22
Anomalous fast magnetic field penetration
s68 1010
• Current channel: >> (c/pe) ???
• Energy dissipation mechanism ???
Relativistic S-band magnetron
Typical framing image (10ns) of the explosive plasma emission
Linear Induction Accelerator•The accelerator pulse: 450kV, 4kA, ~100ns.
•The microwave pulse is 250 MW lasting ~70nsTypical voltage, current and MW waveforms
• To increase efficiency of microwave generation to 40 % and to achieve microwave power of 400 MW
• To achieve 1 GW microwave power in compressor with optimal coupling
Purpose:
Relativistic double gap vircator•The accelerator pulse: 550kV, 12kA, ~400ns.
•The microwave pulse
• is 200 MW, ~200ns
External view of the metal-dielectric, carbon fiber, and velvet cathodes (left-to-right).
(a) Waveforms of the voltage and current. (b) RF signal and its FFT. (c) Diode impedance. (d). Radiation spectrum
Purpose:
• To avoid plasma formation at the surface of the cathode screen electrode• To increase duration of the microwave pulse up to 400 ns• To obtain microwave pulse with energy of 100 J (400 ns, 250 MW)
• Underwater Electrical Wire Explosion
Earliest work on exploding wires was undertaken in Holland by Martinus van Marum in 1790 (http://chem.ch.huji.ac.il/history/marum.html)
135 Leyden jars1 kJ stored energy
1 m wire
Two frame (5 ns) images with 300 ns intervalThe
wire
Streak or Framing Camera + CCD
Time Delay Generator
HV Pulse Generator
Mirror
Flash Lamp,
Laser
Wire electrical explosion – a spiky change in the physical state of the metal as a result of intense energy input due to pulsed current with density >106 A/cm2
Current density: 106 – 1010A/cm2. Current pulse duration: 10-4 – 10-8 s.
Power: 106 – 1013 W. Delivered Energy: 102 – 106 J
Shock waves
Discharge plasma channel
Background medium: vacuum, gas, liquid
Wire explosion in water
Basic Fundamental Research
),( p ),(
112
T
r
Ze
D
Phase transitions: solid state liquid gas plasma
• Ultra-fast heating of metals: dT/dt > 1011 0K/s • Magnetic field: 107 G Energy density: 1011J/m3
Equations of State at extreme conditions (pressure: Mbar, temperature: 104 K)
),( Tf ),( Tfp Pressure Density Temperature Conductivity Internal energy Thermal conductivity
• Non-ideal plasma (high density, low temperature)
Potential energy of Coulomb interaction Thermal energy
Resistivity and thermal conductivity – differ strongly from the case of ideal plasma
T
Ze
kTme
2
3
V. Fortov and I.T. Iakubov, The Physics of Non-Ideal Plasma ( World Scientific Publ., NJ, 2000)
Classical plasma
Applications• High-power radiation sources (visible, UV range) : P >109 W
• Lasers (1000 Ǻ) & Pumping of gaseous and ruby lasers (intensity an order of magnitude greater than that obtained from Xe flash lamps)
• Pulsed neutron source [CD2 or LiD wires: up to 1012 1n0/pulse: NRL (650kA, 100ns)]
• Powerful soft x-ray sources (Lebedev Physical Institute, Cornell University)
• Nano particles (1 – 100 nm) of different metals
• Point-like source 10 m
• Time duration 10 ps – 200 ps
• Soft x-ray energy 2 – 15 keV
• Hard x-ray energy 25 - 80 keV
Current : 300 kA, 100 ns
• Shock waves: underwater electrical wire explosion
• High-current opening switch (high-voltage generator)
0
10
20
30
Prim
ary
curr
ent [
kA]
0
300
600
Virc
ator
volta
ge [k
V]
0
5
10
0 500 1000 15000
200
400P = 120 MW
Primary voltage: 70 kV. Storage capacitor: 3 F. 20 Cu-wires 50 m.
Time [ns]
MW
pow
er
[W/c
m2 ]
Vir
cato
rcu
rren
t [kA
]
• High-current and high-voltage generators (>106V, 104A, 10-7s)
)(dt
dLI
dt
dIL
dt
d
Main Obstacles in Electrical Wire Explosion in vacuum/gas
1. Shunting of the Discharge. The best energy deposition in
vacuum recently achieved by Sarkisov et al.* was 20 times the
atomization enthalpy.
2. Fast plasma expansion (107 cm/s) in vacuum limits
energy density input
3. Radiation cooling in vacuum wire explosion limits
plasma temperature
4. Fast growing plasma instabilities and charged particle
emission
Advantages of the Underwater Electrical Wire Advantages of the Underwater Electrical Wire ExplosionExplosion
Shunting of the discharge is prevented due to:
1. High breakdown voltage of the water medium (>300 kV/cm).
2. High pressure of the adjacent water layer (>10 kBar) increases breakdown voltage.
Increase in the temperature of the wire plasma is achieved by:
1. High resistance of the water to compression limits the wire expansion and leads to the increase in the current density.
2. Substantial decrease in the energy loss to the shunting channel and to radiation (water “bath” effect).
Underwater Electrical Wire Explosion (UEWE)Underwater Electrical Wire Explosion (UEWE) High Density Non-Ideal Plasma High Density Non-Ideal Plasma
Ultra High Pressure at the axis of Converging Cylindrical Ultra High Pressure at the axis of Converging Cylindrical
Shock Wave produced by Shock Wave produced by Underwater Electrical Wire Underwater Electrical Wire ArrayArray
ExplosionExplosion
Stored energy: W ≤ 4.5 kJ Voltage: V ≤ 30 kV Peak current: I ≤ 400 kA Capacitance: C =10 μF Self-inductance: L= 60 nH Power:
Microsecond Timescale GeneratorMicrosecond Timescale Generator
8 2 5 10 A/cm dI
Jdt
113 10 A/s0 2 4 6
0
50
100
150
200
250
0 2 4 6
0
5
10
15
20
Cur
rent
[kA
]
Time [s]
Vol
tage
[kV
]
9P = 5×10 W
0.0 0.2 0.4 0.6
0
10
20
30
40
50
Time [s]
Cur
rent
[kA
]
0
20
40
60
80
100
V [kV
]
12 8 210 A/s 10 A/cmdI
Jdt
Nanosecond Timescale GeneratorNanosecond Timescale Generator Stored energy:
Voltage:
Peak current:
Wave impedance:
Power: 0 1.7 Z
240 kVV 80 kAI
0.7 kJW
93 10 P W
MA Generator (with Institute of High Current Electronics, RAS)
12 10 25 10 A/s 10 A/cmdI
Jdt
• Stored energy: 9.5 kJ• Current amplitude: 900 kA• Rise time: 300 ns• Power: 60 GW
• Electrical probes: voltage & current monitors
• Electro – mechanical pressure gauges
• Optical: Schlieren & Shearing Interferometry
• Fast streak and frame shadow imaging
• Fast photodiodes & narrow band interference filters
• Visible range spectroscopy
Diagnostics Tools Diagnostics Tools
1 2 3 4 5 6 70.0
0.8
1.6
2.4
Ele
cri
cal
Inp
ut
En
erg
y [
kJ]
Ele
cri
cal
Inp
ut
Po
wer
[GW
]
0.0
0.2
0.4
0.6
En
erg
y o
f the W
ate
r Flo
w [k
J]
Electric measurement & Hydrodynamic calculationCu Wire 510µm, 85mm in length
0.0 0.2 0.4 0.6 0.8
0
20
40
Time [s]
Cur
rent
[kA
]
0
40
80
Resistive V
oltage [kV]
Cu Wire 100µm, 50mm in length Microsecond timescale UEWE Nanosecond timescale UEWE
μsec nsec Stored Energy [kJ] ~ 7.0 ~ 0.7 Current Rise Rate [A/s] ~ 10 10 ~ 10 12
Maximal Electrical Input Power [GW] ~ 2.0 ~ 6.0 Maximal Energy Deposition [eV/atom] ~ 10 ~ 60-200 Maximal Generated SW Pressure [kBar] ~ 10 ~ 100 Maximal DC Temperature [eV] ~ 1.0 ~ 7.0
A. Grinenko, Ya. E. Krasik, S. Efimov, A. Fedotov, V. Tz. Gurovich and V.I. Oreshkin, Physics of Plasmas 13, 042701 (2006).
Water Vaporization by the Heating WireWater Vaporization by the Heating Wire
• A thin water layer (~ 1-5 µm) adjacent to the heating wire remains in the
liquid state during all the heating process for heating rates: Tc/0.5μs
109 oC/s (Tc=420oC is the critical temperature of the water).
The phase state trajectory of a < 5 μm water layer for different heating rates
100 200 300 400
10-1
100
101
102
10-1
100
101
102
Vapor
Water(b)
Pre
ssur
e [B
ar]
Temperature [ oC ]
Vapor
Water
Saturation curve t
max = 24 ns
tmax
= 100 ns t
max = 400 ns
(a)
Pre
ssur
e [B
ar]
The phase trajectory lies above the saturation curve during the heating process NO BOILING
No evidence of shunting channel observed !!!Power < 6 GW, Energy < 0.7 kJ
T t
T t2
Water “Bath” EffectWater “Bath” Effect• For I3 MA wire explosion, the >13.5 eV radiation from the wire ionizes the water. This
causes current redistribution between the discharge channel and the water.
• The energy lost by the discharge channel to the water plasma channel is re-absorbed
due to radiation heat transfer from the water-plasma to the discharge channel
0 30 60 90 120
0
3
6
9
12
a)Cu wire, diameter 0.5 mm
Thermal Energy
Radiation Energy
Ene
rgy,
kJ/
cm
Time, ns
Time dependence of thermal energy and radiated energy of the DC. Negative values of radiated energy correspond to absorption.
Maximum fraction of the shifted current is 30%
50 100 150 200 2500
20
40
60
80
100
Inpu
t Ene
rgy
per
Uni
t Len
gth
[J/c
m]
7
6
2
1 3
4
5
x109 [Pa]
Energy density Energy density scalingscaling
The deposited energy per unit length is proportional to Π (power rate per unit length)
0
maxw
dP
l dt
Shearing interferometry combined with shadow imaging,
hydrodynamic and optical simulations allows estimation of the
efficiency of the energy transfer to the generated SW as
~ 15%.
UEWE: Radiation Short pulse emission (300 ns)
(during the wire explosion from the wire surface)
Long pulse emission (100 μs) is a result of a growth of emitting area due to creationof micro-particles and their relatively long cooling
0 40 80 120 160 200
6000
9000
12000
15000
0
2
4
6 Tcathode Tanode
Tem
pera
ture
[K
]
Time [ns]
Pow
er [
GW
]
Spectrally resolved radiation
300 400 5000
30
60
90
120
150 Calculated spectrumExperimental spectrum
at t=100ns
Inte
nsit
y [a
.u.]
Wavelength [nm]
MHD CalculationsMHD Calculations
10
r v
t r r
1z
v v pv j B
t r r c
21 1zrv j Tv p r
t r r r r r r
1; ;
4z
z
rBB E cj
c t r r r
z zj E
, ; , ;P P T T
, ; , ;
Mass conservation
Momentum conservation
Energy conservation
Maxwell equations
Ohm law
Equations of state
Transport parameters
Surface temperature ~ 2 eVOn axis pressure ~ 400 kBar
Experimental & MHD calculation results of the explosion of Cu (L=100mm, Ø100μm) wire
Solid curves – experimental results
Dashed curves – MHD calculation.
MHD CalculationsMHD Calculations
Time [ns]
0 10 20 30 40
1
2
3
4 43
21
5
cr
1016
x[1/
sec]
103x[1/(cm)]
max max2
max max
w
w
L I j
R V E
Parametric SimilarityParametric SimilarityCylindrical Geometry
0 4 8 12 16 20
0.0
0.4
0.8
1.2
Rmax
= 7.5 mm R
max = 5.0 mm
Rmax
= 2.5 mm
Max
imal
Pre
ssur
e [M
Bar
]
ET / (L
w t
f) [kJ/cm s]
ImplosionImplosionDue to the cumulation effect of the converging SW it is possible to
achieve ultra-high pressure at the axis of implosion
Self-similarity problem
R t
• In the case of diverging SW (total energy of the
explosion is conserved in the volume limited by
the SW) the parameter can be determined using
dimensional analysis of physical parameters
• In the case of implosion the energy in the volume
between the SW and the exploding liner is not
conserved: thus cannot be determined without
hydro-dynamic numerical simulations.
2(1 1/ )
20 0
T SWSW
E RP
R R
Initial energy
Initial radius
α ~ 0.6 - spherical implosion
α ~ 0.75 - cylindrical implosion
A. Grinenko, V. Gurovich,Ya. Krasik, Phys. Plasmas 14, 012701 (2007). V. Gurovich, A. Grinenko, Ya. Krasik, PRL 99, 124503 (2007).
Time [s]
Rad
ial
Dis
tan
ce [
mm
]
0 2.5 5.1 7.7 10.2
5.02.50.0
2.5
5.0
Streak image of the implosion with a cylindrical wire array
Implosion – Experimental Setup
Imploding array
Target
Implosion wave
Ya. E. Krasik, A. Sayapin, A Grinenko, and V. Tz. Gurovich, Phys. Rev. E 73, 057301 (2006).
40ty 50m dia Cu-wire array
Cylindrical SW Implosion
40 Cu wires (Ø0.1mm) array (R0 = 2.5 mm)
• The pressure is estimated as ~400 50 kbar at r = 0.1 mm (4.5 kJ microsecond setup) Initial SW pressure generated by the wire explosion is 10kbar.
Damping of initial non–uniformity of
SW front is evident in 2D simulations
0 1 2 30
2
4
6
8
Mac
h nu
mbe
r
Radius [mm]
P=20M(M-1)P=400 kbar, =1.85
0, R=0.1mm
1 1/ , 0.68M R 3/2
min 2
2 ( 1) 2
2(1 )
0.69 0.71 for 7.5 8
Landau & Stanukovich:
300 , t 10ft ns ns
The Model Includes:• Bremsstrahlung radiation losses• NO molecular, electron or
radiative heat transfer• NO instabilities• NO energy transfer by α particles
D-T Gas Mixture Target IgnitionD-T Gas Mixture Target Ignition
Rsh [mm] Rt = [mm] ET = [kJ] Reaction Yield
x1013
(1) 5.0 0.25 31.2 4.23
(2) 5.0 0.25 10.8 7.88
(3) 7.5 0.50 36.5 14.7
(4) 5.0 0.50 10.2 1.05
The calculated DT reaction yield for various implosion parameters: