Pulsed-Power Plasma
and its Applications
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
What is Pulsed Power ?
Power  109-1014W,
Current  104-107A,
Energy  105-107eV
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
• High-Power Bremsstrahlung Sources (Electron beams)
Dose ~ Ee2.8Ie (HERMES III: 20MeV, 700kA, 30ns 100 kRad at 500 cm2)
• High Intensity Neutron Fluxes ( Ion beam  1013 1n0/pulse)
• Strong Shock Wave Generation (electron and ion beams)
Pressure ~ Pb /(S); Pb ~ 1013 W/cm2  Pressure ~ 10Mbar
• High-Power Microwaves (Microwave power  10 GW)
• High-Power Pulsed Gaseous Lasers
• Strengthening and Modification of Materials
• Thin Film Preparation
)‫כור היתוך (ריאקציה מיזוג גרעיני‬
q1q2
(  e) 2
U  ke
 ke
 0.14MeV
R
R
3
U  k BT  T  5.6 108 0 K
2
‫טריטיום‬
‫דאיטריום‬
2
1
H  21 H 23 He 01 n Q  3.27 MeV
2
1
H  21 H31 He11 H Q  4.03 MeV
2
1
H  31 H 42 He 01 n Q  17.59 MeV
Confinement Fusion
2H
1
+3H1  4He2 (3.6 MeV)+1n0 (14 MeV) [Energy: 1 kg  1014 J]
The volume rate of fusion reactions: f  nD nT
 DT V  0.25ne2  DT V
fEDT ( )  Ploss
Confinement time
E 
3kTne
W[J ]
12kT


n


e E
Ploss [ J / s] 0.25ne2  DTV EDT
 DTV EDT (3.6MeV )
At T = 25 keV
T
 min  ne E  1.5 1014 s / cm3  ne ET  1015 s  keV/cm 3 
 DTV
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 – 41010 J
Inertial Confinement Fusion
Confinement time: time it takes sound waves to travel across the plasma
 E  R / kT / M i
ne E  1.5 1014 s / cm3
  R  1g / cm2
P  V   Const 
PV

3


Const

n

R

Adiabatic compression:
T
T  V  1  Const

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 of
the fusion target forming a
surrounding plasma layer
Compression
Target is compressed
by plasma expansion
Ignition
The fuel core reaches
104 of T-D density
and ignites at 10 keV
Burn
Thermonuclear burn spreads
through the compressed T-D,
yielding the input energy.
• Electron Beams • Laser Beams (NIF: Lawrence Livermore National Lab)
• Soft X-rays (Z-pinch: Sandia National Lab)
• Ion Beams
Z-pinch
USA, UK, France,
Russia, Israel,
Japan, China
Electric field
energy
WE  CU 2 / 2
11 MJ
Magnetic field
energy
WM  LI 2 / 2
Kinetic energy
WK  NM iVi 2 / 2
V
7.5 107 cm / s
Thermal energy
WT  NkT
Soft X-ray
radiation
2 MJ, 290 TW
20MA 150 ns
Hohlraum radiation
temperature  200 eV
Sandia National Laboratory
40mm Tungsten wire
Array 240 5m  wires
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
Z-accelerator
M. G. Haines, et al. Phys. Plasmas 7, 1672 (2000)
High-current electron beams
Planar diode
EA = EC

Qi=Qe  Iete = Iiti  Ie = Ii(mi/me)1/2
1/ 2
m 
  4  4
 4je,i  e,i 
Ve,i
 2e 
je,i
I e,i  S
• Alfven current: IA = 17b [kA]
2
 1 / 2
 3/ 2
e 1/ 2
)
9 me,i
(d  V plt )2
(
• Space-charge-limited current: Is-ch= (mec3/2e)( 2/3 - 1)3/2/[1+2ln(R/rb)]
• Lawson current: IL = IAb2(b2+ f - 1)-1, f = (ni/ne)
High-current electron diode
Example of closure of Anode-Cathode gap by plasma
dac= 20mm, Ua= 180 kV, I = 2.5 kA. Frame 10 ns
Potential distribution in the plasma prefilled
diode
Relative potential
1.0
80 ns
180 ns
280 ns
0.8
0.6
0.4
0.2
0.0
0
1
2
3
4
Distance from the anode (cm)
5
High current ion beams
Planar bipolar diode: Ii = Ie(me/Mi)1/2
It is necessary to increase life-time of electrons in the anode-cathode gap
Reflex systems
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 Plasma
The 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
Carbon fiber cathode
Formation of emission centers depends
strongly on the growth rate of the electric field
d  m l
l
1


j fe ( ) 

dt  f d AC 0
0
Flashover Plasma (ferroelectric plasma cathodes)
Polarization Reversal model
Light Emission (BaTiO3 cathode, 1700)
Frame 5 ns
Plasma model
POS
Electron beam
current [kA]
current [kA]
POS voltage
[kV]
Plasma Opening Switch
400
200
0
40
20
0
20
10
• Anomalous fast magnetic field penetration
Classical diffusion time:

4L2
c 2
0
0
200
400
600
800
1000
Time [ns]
-8
-6
 106  104 s Experiment: 10 - 10 s
• Fast increase of the plasma resistivity: 107-109 W/s
• Generation of high-current electron and ion beams
1200
Anomalous fast magnetic field penetration
• Electron Magnetohydrodynamics (Hall effect
)B / t  (c / 4e)  [ (  B)  B]  ( c 2 / 4 ) B
ne
•
cB 2
1
Vc 
r r ( 2 )  107  108 cm / s
4e
nr
• Current channel: d >> (c/wpe) ???
• Energy dissipation mechanism ???
8
6
  10  10 s
Relativistic S-band magnetron
Linear Induction Accelerator
•The accelerator pulse: 450kV, 4kA, ~100ns.
•The microwave pulse is 250 MW lasting ~70ns
Typical voltage, current and MW waveforms
Typical framing image (10ns)
of the explosive plasma emission
Purpose:
• 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
Relativistic double gap vircator
•The accelerator pulse: 550kV, 12kA, ~400ns.
•The microwave pulse
• is 200 MW, ~200ns
(a) Waveforms of the voltage and current. (b) RF signal and its FFT.
(c) Diode impedance. (d). Radiation spectrum
External view of the metal-dielectric, carbon fiber,
and velvet cathodes (left-to-right).
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
1 m wire
135 Leyden jars
1 kJ stored energy
Earliest work on exploding wires was undertaken in Holland by
Martinus van Marum in 1790 (http://chem.ch.huji.ac.il/history/marum.html)
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
Background medium: vacuum, gas, liquid
Flash
Lamp,
Time Delay
Generator
Wire explosion in water
Laser
The
wire
HV Pulse
Generator
Two frame (5 ns) images
with 300 ns interval
Shock waves
Mirror
Streak or Framing
Camera + CCD
Discharge plasma channel
Basic Fundamental Research
• Ultra-fast heating of metals: dT/dt > 1011 0K/s
• Magnetic field: 107 G Energy density: 1011J/m3
Phase transitions: solid state
liquid
gas
plasma
Equations of State at extreme conditions (pressure:  Mbar, temperature: 104 K)
Pressure Density Temperature
p  f (, T )
Conductivity
Internal energy
   ( , p)
Thermal conductivity
  f (, T )
   ( ,  )
• Non-ideal plasma (high density, low temperature)
Potential energy of Coulomb interaction
Thermal energy
Classical plasma
 Ze2  1
 T  1
  
 rD 
 

Ze 2
e 

T
3kTm
Resistivity and thermal conductivity – differ strongly from the case of ideal plasma
V. Fortov and I.T. Iakubov, The Physics of Non-Ideal Plasma ( World Scientific Publ., NJ, 2000)
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)]
• Nano particles (1 – 100 nm) of different metals
• Shock waves: underwater electrical wire explosion
• High-current opening switch (high-voltage generator)
• Powerful soft x-ray sources (Lebedev Physical Institute, Cornell University)
Current : 300 kA, 100 ns
• 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
and high-voltage generators (>106V, 104A, 10-7s)
d
dI
dL
 
 ( L  I
)
dt
dt
dt
Primary
current [kA]
0
600
Vircator
current [kA]
Vircator
voltage [kV]
Primary voltage: 70 kV. Storage capacitor: 3 F
20 Cu-wires 50 m.
30
20
10
300
0
10
5
0
MW power
2
[W/cm ]
• High-current
400
P = 120 MW
200
0
0
500
1000
Time [ns]
1500
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
Underwater Electrical Wire Explosion (UEWE)
 High Density Non-Ideal Plasma
 Ultra High Pressure at the axis of Converging Cylindrical Shock
Wave produced by Underwater Electrical Wire Array Explosion
Advantages of the Underwater Electrical Wire Explosion
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).
Microsecond Timescale Generator
 Stored energy:
20
200
15
150
10
100
50
5
0
0
0
2
Time [s]
4
Voltage [kV]
Current [kA]
250
6
W ≤ 4.5 kJ
 Voltage:
V ≤ 30 kV
 Peak current: I ≤ 400 kA
 Capacitance: C =10 μF
 Self-inductance: L= 60 nH
 Power: P = 5×109 W
dI
 3  1011 A/s J  5 108 A/cm 2
dt
50
40
30
20
10
0
100
80
60
40
20
0
V [kV]
Current [kA]
Nanosecond Timescale Generator
0.0
0.2
0.4
0.6
Time [s]
 Stored energy: W  0.7 kJ
V  240 kV
 Peak current:
I  80 kA
 Wave impedance: Z  1.7 W
0
P  3 109 W
 Power:
 Voltage:
dI
 1012 A/s J  108 A/cm 2
dt
MA Generator (with Institute of High Current Electronics, RAS)
• Stored energy: 9.5 kJ
• Current amplitude: 900 kA
• Rise time: 300 ns
• Power: 60 GW
dI
 5 1012 A/s J  1010 A/cm 2
dt
Diagnostics Tools
• 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
Microsecond timescale UEWE
Nanosecond timescale UEWE
1.6
0.4
0.8
0.2
0.0
0.0






1
2
3
4
5
6
7
Stored Energy [kJ]
Current Rise Rate [A/s]
Maximal Electrical Input Power [GW]
Maximal Energy Deposition [eV/atom]
Maximal Generated SW Pressure [kBar]
Maximal DC Temperature [eV]
Current [kA]
Elecrical Input Energy [kJ]
Elecrical Input Power [GW]
0.6
Energy of the Water Flow [kJ]
2.4
Cu Wire 100µm, 50mm in length
40
80
20
40
0
0
0.0
0.2
μsec
~ 7.0
~ 10 10
~ 2.0
~ 10
~ 10
~ 1.0
0.4
0.6
Time [s]
Resistive Voltage [kV]
Cu Wire 510µm, 85mm in length
Electric measurement & Hydrodynamic calculation
0.8
nsec
~ 0.7
~ 10 12
~ 6.0
~ 60-200
~ 100
~ 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 Wire
Pressure [Bar]
Pressure [Bar]
The phase state trajectory of a < 5 μm
water layer for different heating rates
2
(a)
10
Water
Vapor
1
10
0
10
-1
10
2
10
No evidence of shunting channel observed !!!
Power < 6 GW, Energy < 0.7 kJ
Tt
(b)
Saturation curve
tmax = 24 ns
tmax = 100 ns
tmax = 400 ns
Water
1
10
0
Vapor
10
-1
10
T  t2
100 200 300 400
o
Temperature [ C ]
• 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 trajectory lies above the saturation curve during the heating process
NO BOILING
Water “Bath” Effect
• For I3 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
a)
Cu wire, diameter 0.5 mm
12
Thermal Energy
Energy, kJ/cm
9
6
3
Radiation Energy
0
0
30
60
90
120
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%
Input Energy per Unit Length [J/cm]
Energy density scaling
100
7

80
60
5
40
20
1
0
50
Shearing


lw  dt  max
The deposited energy per unit
length is proportional to Π
(power rate per unit length)
6
2
4
 0  dP 
3
100
150
200
9
x10 [Pa]
interferometry
250
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)
Spectrally resolved radiation
(during the wire explosion from the wire surface)
Intensity [a.u.]
150
Calculated spectrum
Experimental spectrum
at t=100ns
120
90
60
30
0
300
500
Wavelength [nm]
Long pulse emission (100 μs)
Tcathode
Tanode
15000
4
12000
2
9000
0
6000
0
40
80
120
Time [ns]
160
200
Power [GW]
6
Temperature [K]
is a result of a growth of emitting area due to creation
of micro-particles and their relatively long cooling
400
MHD Calculations
 1   r  v 

0
t r r
v
v
p 1
   v    jz B
t
r
r c
Mass conservation
Momentum conservation


1   rv  jz2 1   T 
  v   p
 
 r
t
r
r r
 r r  r 
1 B Ez

;
c t
r
c   rB 
jz 
;
4 r r
jz   E z
Energy conservation
Maxwell equations
Ohm law
P  P  ,   ; T  T  ,   ;
Equations of state
    ,   ;     ,   ;
Transport parameters
MHD Calculations
Experimental & MHD calculation results of the
explosion of Cu (L=100mm, Ø100μm) wire
Solid curves – experimental results
Dashed curves – MHD calculation.
4
4
3
3
16
cr 10 x[1/sec]
Time [ns]
 
1
2
2
1
Lw I max
jmax

Rw2 Vmax Emax
5
0
10
20
3
30
 10 x[1/(Wcm)]
40
Surface temperature ~ 2 eV
On axis pressure ~ 400 kBar
Implosion
Due to the cumulation effect of the converging SW it is possible to achieve
ultra-high pressure at the axis of implosion
Self-similarity problem
Maximal Pressure [MBar]
Parametric Similarity
R  t
Cylindrical Geometry
• In the case of diverging SW (total energy of the
explosion is conserved in the volume limited by
1.2
the SW) the parameter  can be determined using
dimensional analysis of physical parameters
0.8
Rmax = 7.5 mm
Rmax = 5.0 mm
Rmax = 2.5 mm
0.4
0.0
0
4
8
12
16
ET / (Lw tf) [kJ/cm s]
20
• 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.
Initial energy
 E  R 
PSW   T2   SW 
 R0   R0 
α ~ 0.6 - spherical implosion
α ~ 0.75 - cylindrical implosion
2(11/ )
Initial radius
A. Grinenko, V. Gurovich,Ya. Krasik, Phys. Plasmas 14, 012701 (2007). V. Gurovich, A. Grinenko, Ya. Krasik, PRL 99, 124503 (2007).
Implosion – Experimental Setup
Imploding
array
Implosion
wave
Target
Radial Distance [mm]
40ty 50m dia Cu-wire array
5.0
2.5
0.0
2.5
5.0
0
Streak image of the implosion with a
cylindrical wire array
2.5
5.1
Time [s]
Ya. E. Krasik, A. Sayapin, A Grinenko, and V. Tz. Gurovich, Phys. Rev. E 73, 057301 (2006).
7.7
10.2
Cylindrical SW Implosion
40 Cu wires (Ø0.1mm) array (R0 = 2.5 mm)
t  300ns, t f  10ns
Mach number
Damping of initial non–uniformity of
8
P=20M(M-1)
P=400 kbar, =1.850, R=0.1mm
6
M
4
11/
R
,  0.68
2
0
0
1
2
3
SW front is evident in 2D simulations
Landau & Stanukovich:
2  (  1)  2 3/2
 min 

2
2(1   )
 0.69  0.71 for   7.5  8
Radius [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.
D-T Gas Mixture Target Ignition
The Model Includes:
• Bremsstrahlung radiation losses
• NO molecular, electron or
radiative heat transfer
• NO instabilities
• NO energy transfer by α particles
The calculated DT reaction yield for various implosion parameters:
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
0.50
10.2
1.05
(4)
5.0