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: