J. Plasma Fusion Res. SERIES, Vol. 2 (1999) 398-401

Diamagnetic Cavity of Plasma Clouds Expanding in
Magnetized MediaZAKHAROV Yuri P., MELEKHOV Alexandr V., ORISHICH Anatoli M.',
PONOMARENKO Amold G., POSUKH Vitali G. and SHAIKHISLAMOV Ildar F.
Institute of lnser Physics, Novosibirsk, 630090, Russial Novosibirsk State University and Institute of Theoretical& Applied Mechanics, Novosibirsk, 630090, Russia(Received: 8 December 1998 / Accepted: 24 August 1999)

Abstract
Basic properties of the diamagnetic cavity created by spherically expanding clouds of exploding
plasma in various magnetized media are studied as a result of the series experiments at large-scale "KI-1" facility with laser-produced plasma clouds of energy up to 300 J in the magnetic fields up to 2 kG.
The cases of uniform and dipole fields were investigated to simulate an explosive-type cosmophysicalphenomena and some schemes of the direct conversion of ICF-energy.

Keywords:
laser-produced plasma, magnetic fields, space and lCF-phenomena

1. Introduction

MM background and its density gradient Vn-( | lor JB) have been investigated [4]. Some preliminary data on
the 2D-structure of diamagnetic cavity in both uniform

Diamagnetic cavity (DC) of exploding plasmas
formed during their expansion into magnetic field plays
a crucial role in the most key processes of interaction
between plasma and surrounding magnetized media.

and dipole vacuum magnetic field Ba were obtained in aseries of <<Cavity> experiments [5-10] and here we will

Such plasmas with kinetic energy Es could bepresent their completed results in more details.

decelerated by magnetic pressure B2/8n and stopped in2. uKI-7> Laser Facility and Magnetic Field

vacuum uniform magnetic field 86 at the radius R5 =(3BolBo\tt3, equal to the maximum cavity size R". inthis case [1], namely due to DC creation and fields'
exclusion by plasma. The unique parameters of "KI-L"

Measurements
The multi-purpose "KI-l" laser facility [2,11]
consists of a large-scale (Ol.2m x 5m), high-vacuum
interaction chamber and the system of CO2-lasers withfacility allowed us to study the general 1D-properties of
diamagnetic cavity in uniform magnetized media (MM)in the experiments [2,3] on spherically-symmetrical

output energy - I kJ for producing quasi-spherical LPC
with moderate velocity y0 - 100-200kmls, mlz - 2-3
amu and energy E0 up to 300 J needed for simulation of
space [2,6,11] and ICF [5,9] phenomena at small valuesof e5 < 0.3. The optical system provides two-sided andexpansion of Laser-produced Plasma Clouds (LPC) witha number of ions Ni (of the mass-nt and charge-z) under

the condition of rather strong ion magnetization €u = Rn/

Ru < I (for ion Larmor Rn = trrcVolzeB6), which isneeded for effective plasma-MM interaction and LPC
deceleration at R". = Ro. Also an influence of ionizedmulti-staged irradiation of small-size spherical orfilament Nylon6 pellets. The chamber is supplied by@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author's e -mail: zakharov@ plasma.nsk.ru
398

Zakharov Y.P. et al., Diamagnetic Cavity of Plasma Clouds Expanding in Magnetized Mediasources of an axial uniform B6-field (up to I kG), dipole
B6-field (with M > l0 MG* cmr) and @-pinch typetime [3] a very thin width of skin-layer 6 = 2clotp. and0I"'= 0.5 while in other experiments F2,l3l it was not
more than O.3.In "Cavity" experiments a real sphericalshape of DC (Fig. l) was registered at early times ofexpansion as well as a whole D6-character of its B(r, 0)disturbances. It allowed us to develop contactless
method [8] of <<Remote Magnetic Probe>> (RMP) todetermine the size R" of DC via measurements of RMP-

source of background plasma with n* up to 5*l0r3cm-3.
The <Cavity> experiments were done with LPC (Eo l0J) expanding into the dipole [6,10] and uniform [6-9]magnetic fields (86 = l-2kG and B0 = 40-800G) with
0.7 < e6 < 2. For magnetic field measurements we used
3-component B-dote probe with high-frequency (50signal B1n(ro) at distances rp ) R" and calculation offtcMHz) coils of diameter 3-5mm with electrostatic [3,10]
shielding, inserted into (5-7)mm-diam isolators. A set ofsuch probes with digitalization system allow us to obtainthe grid (- I cm* I cm) of 2D-distributions of vectors

as R" = rn(2pt)"t. The results of direct measurementsof R"- (for level d, = 0.5 at rp < R") agree rather wellwith those of RMP (Fig. 2). But both of them become

trt o, E = io + Ai and the levels of s = lByn$or o6 =very different from the corresponding SSM's cavity data(R"- = ftu) in the range of e6 > 1.5 (80 < 100G, E0 = 8J). The reason is a fast B-field penetration into plasma

f1r;yf$1r;of the fields' exclusion inside of plasmas
and of its disturbance B = ILBVBB outside the LPC (forinitial field do). ttt" suitability of the whole[3] with very high effective collision frequency ofmeasurements' procedure was tested by the control ofmagnetic flux conservation and by comparison of theelectrons vun= Ean(6 - 0.3 in DC skinJayer) probably
related to observed lower-hybrid turbulence (LHT). Dueto this reason only at early-stage of DC expansion thelaw of R"(r) dynamics could coincide with the plasma
radius R(/) and both of them could be described [9] inthe range ar < I by SSM deceleration law in thedimensionless I l] form:!6values of DC currents determined from the data on
AB, obtained both inside and outside (see below) ofLPC.

3. Diamagnetic Cavity in Vacuum Uniform
Magnetic Field
According to the model [] of plasma cloud as,-\- nlo.zx, ) tor<<superconducting sphere>> (SSM) the magnetic fieldshould be excluded down to B = 0 inside of DC (andplasma) boundary R" and should have outside it thedipole-like disturbance trt=io, which is described bythe magnetic moment of DC currents pu = -B$R"3/2. So,along the isu=R/Ru< I and tr=tVolRv(1)

After the time 16 = 1.5 the boundaries of plasma and DC
begin diverge as fi goes over fi5 ( due to flute instability
l2,l2,l3l of plasma) and as R" stops at R"- = (0.8-0.9)
R6 (due to &broadening t3,8,91) and further collapses.

f dB direction (e = ftD) the fieldcompression should be FL= 0.5(rlR")3 and in others B =B1(1 + 3cos20)r/2. Earlier we have obtained for the firstt= 7 lt s
a=0.70246810

100Bo,Yr cm

G| 1000
Bd, GFig. 2 Dependence of maximum cavity size B* upon theplasma energy Eo and various magnetic fields 8.

Fig. 1 Diamagnetic cavity evolution in uniform Ao-field.
399

Zakharov Y.P. et aI., Diamagnetic Cavity of Plasma Clouds Expanding in Magnetized MediaY

1.2o - "KI-I" exp.

cO - other

1.0

0.8

0.6

()

0.4
0.2

I - CRRES, AMPTE

0.00|

2rd34Cl - comp. simul.
52ev3Fig. 3 Dynamics of cavity boundary across ft-field.

4Fig. 4 Dimensionless scaling of the cavity <<lifetime> invacuum uniform magnetic field (N-data of H.

The whole measured DC dynamics in the range e6 > I
could be roughly described by the usual field diffusion
model with 6 = ''[c'tl4tto and d = nre2/mrvr6. Using thesimple formulae [3] ft"(t) = Vot-6(t) we obtain a new,diffusion law of DC evolution:

Nakashima, 1998).

natural (or ICF) plasmas that provides the base tosimulate them by LPC.

so=?u-0.25t1
forTo=1YolRd < I andsd=Rcl&4. The Effects of Fields' Non-Uniformity andlonized Backgrounda)

That gives another maximum size of DC t3l R"- = Ra

SSM's based analysis and calculations [5,15] of thevia a new scale of the problem R6 = (3exN1Vo/

plasma stopping radius,R-(0) in the dipole field shows

l6c(Bo1rt2 = R6/{e5 and corresponding DC <<lifetime>>that in sectorial approximation it depends only from theparameter E -- 3EoRAlMz = (Rb/R0)3 and angle Efifio(where R6 is the radius between dipole M and explosionpoint) via unified equation F(tp, R^lRs) = a. It gives R= Rr(Ba) for e << I while R- -e - (breakout of plasma
into -VBfr direction) for e > O.l.ln <KI-l> experiments

T.d - 3-4 R6/Ve (determined only by turbulent
diffusion). The formulae (2) agrees rather well with alldata on DC dynamics at 0 = ttl2 in <<Cavity>>
experiment if one takes 6 = 0.25 (Fig. 3). But along 0 =trl4 (Fig. l) we had observed more faster field[5] the main features of such plasma-dipole interaction
were observed. Besides it, a <<non-sectorial>> effect ofdisplacement of cavity (and plasma) as a whole werepenetration which may be caused by the Hall-effect, that

could appear namely here with the same v"11 = {rd"". In

general, the <<lifetime>) fc of DC, defined indimensionless form as T"= TrVolRn and determined by
the level a = 0.5 of field penetration inside of r - R"^/ 2

registered [6,10] at Q = 30" even for c < 0.1. DC
structure for this regime at Q - 0 (Fig. 5) could beroughly described by sectorial approximation as quasistationary ovoid shape (with R" - R- - R6). It is valid

could be expressed for the diffusion regime (2) by therelation like 7"6 = 3lrtq While for MHD-case in therange t5 << I we could use the scale of <<Alfvenic>>
frequency [4] which describes the DC evolution asstopping (l) at R5 and following inward motion withAlfven velocity that gives us [7] the limiting value 7.0 =3. Therefore, in the intermediate range €b = 1 the curvesy"6 and 66 should transit into each other. The <<KI-|>
results (see O at Fig. 4) and other laboratory (O) or
space experiments (*) and computer simulations ([l)
could be described by such DC <<lifetime>> (T"n -+ T"a)relation in a wide range of conditions of exploding

only liom the initial interaction time /1 - R5/Ys - 0.3 ps
up to 1-1.5 ps, but after that DC goes away withvelocity rather close to its estimation Vsrett3 via theaction of (!aV) Ba-force. In the case of plasma cloud
expansion with super-Alfvenic velocity Vs>C^= Bol(4nm*n*)t/2 into background plasma l2,4,lll two othereffects and DC scales became important: its spatial
12,11,161 on. fr = (3zNi/4trn.)t/3 and its T.-value,
reaching [7] the classic al one 4o"R"2lncz (for Coulomb
conductivity o" of background) due to suppression of400

Zakharov Y.P. et al., Diamagnetic Cavity of Plasma Clouds Expanding in Magnetized Media

t=2.2 ps

ad =o't,=0.tt ltsl
ad =o.s I

a*0.02\l0 cmFig. 6 Simulation of Super-Nova diamagnetic cavity atpresence of ionized background.

Ro=21cm(g=0)
M=12 MG*cnfal., ESA SP-311, Varenna-Abastumany-ESANagoya-Potsdam Workshop on Plasma

Fig. 5 Evolution of diamagnetic cavity in dipole field.

Astrophysics, Noordvijk (ESA, 1990) p.189.

[5] Yu.P. Zakharov, S.N. Nikitin, A.M. Orishich andA.G. Ponomarenko, Book of Abstracts of FourthIntern. Toki Conf. on Fusion and Astrophysical
Plasmas (Toki, 1992) p.47.
[6] V.M. Antonov, Yu.V. Afonin, Yu.P Zakharov,
A.M. Orishich et al., UK Inst. of Physics Conf.

LHT and flutes . In such kind of experiments at <KI-7>on simulation of Super-Nova Remnants (SNR)
dynamics at numbers Mt =VolCt >> I we had realized
for the first time in laboratory [2] the plasma-plasma
collisionless interaction at R - R due to the action ofcurl electric fields. It is possible only under condition e= fnnnn.lfr < I of both kinds of ions magnetization

Series N140, 167 (1995).

[7] Yu.P Zakharov, A.V. Melekhov and A.G.

compression) if expressed in corresponding
dimensionless time t* = tVolR = 1.5-2 which is t = 2 lts
for laboratory and 1500 years of SNR DA530 age,Ponomarenko, Abstr. of IEEE Intern. Conf. onPlasma Science (Santa-Fe, 1994) p.92.
[8] Yu.P Zakharov, A.V Melekhov, S.A Nikitin et al.,Proc. 1996 Int. Conf. on Plasma Physics (Nagoya,1997) v.2, p.l67o.
Yu.P.
Zal,harov, A.G. Ponomarenko, H. Nakashima[9]et al., Proc. 9th Int. Conf. on Emerging Nuclear
Energy Systems, Ramat Gan (Dan Knassim Ltd,expanding with Vs - 5000km/s.
This work was supported by Russian Fund of Basic
Research, Grant N98-02-17 833.

[10] I.F. Shaikhislamov, V.M. Antonov, Yu.P. Zakharov
et al., J. Appl. Mech. Techn. Phys. 36, 488 (1995).

and the formation of DC with R" - R (and B-fieldcompression at its edge, see region I at Fig. 6a). The
measured DC structure is very similar to the observed[17] SNR one (Fig. 6b with region 2 of plasma

1998) v.l, p.384.

Il]Yu.P. Zakharov, A.M. Orishich and A.G.
Ponomarenko, Laser-Produced Plasma andLaboratory Simulation of Non-Stationary Space
Processes (ITAM, Novosibirsk, 1988) p.220 - In

References

lll Yu.P. Raizer, J. Appl. Mech. Techn. Phys. N6, 19(1963) - in Russian (see also NASA fN F-239:

Washington DC, 1964, 20p.).
[2] Yu.P. ZaLharov, A.M. Orishish, A.G. Ponomarenko
et al., ESA SP-251, Joint Varenna-Abastumany

Russian.

[2] G. Dimonte and L.G. Wiley, Phys. Rev. Lett.67,
1755 (1991).

Intern. School & Workshop on Plasma

ll3l B.H. Ripin er a/., Phys. Fluids B5, 3491 (1993).
ll4l L.L. Lengyel, Phys. Fluids 31,1577 (1988).
ll5l S.A. Nikitin and A.G. Ponomarenko, J. Appl.
Mech. Techn. Phys.34, 745 (1994).
116l T.P. Wright, Phys. Fluids 14, 1905 (1971).
ll7lD.K. Milne, Australian J. Phys. 40,771(1987).

Astophysics, Noordvijk (ESA, 1986) p.37.
[3] Yu.P. Zakharov, A.M Orishich, A.G Ponomarenko
and V.G. Posukh, Sov. J. Plasma Phys. 12, 614(1986).

t4l V.M. Antonov, Yu.P. Zakharov, A.M Orishish et401