INSTITUTE OF PLASMA PHYSICS CZECHOSLOVAK ACADEMY OF SCIENCES

GAS-PUFF Z-PINCH EXPERIMENT

A. Krejčí

RESEARCH REPORT

IPPCZ 286 •> November 19M

POD VODÁRENSKOU VEZl 4, i80 69 PRAGUE 8 CZECHOSLOVAKIA GAS-PUFF Z-PIHCH EXPERIMENT

A. Krejčí

IPPCZ-286 November 1988 - 2

1• Introduction

Pinch-effect is the tendency of a current-carrying column of a matter to compress itself towards Its axL&« The implosion is caused by the interaction of the current with the self-magnetic field* The idea of a simple arranged experiment in which the high current (on order of MA) thermo- -insulates the plasma by its own magnetic field and simulta­ neously heats it by both Joule heat and adiabatic compression is very attractive! on this principle the first experimental devices for controlled thermonuclear fusion were constructed in early 1950 s [1, 2 J. But the thermonuclear parameters were not reached. MHD Instabilities of compressed plasma fibre, mainly the m = 0 (sausage) and m • 1 (kink) modes, were the main reason of this failure* In addition, the Joule heating proved to be effective only In the beginning of the plasma implosion, because specific resistivity rapidly decre­ ases during the plasma temperature growth (ij r* T ~^' ). Nevertheless, those experiments demonstrated the Z-pinch as an intense ри1зе X-ray source and at the same time they sti­ mulated the progress of high-power pulse technology and plas­ ma diagnostics.

Recent concept of linear Z-pinch Is different from that in the 1950 s. It is emphasized the second mechanism of heating now, i.e. adiabatic compression, which Is In some respect the opposite pole to the first mechanism. Pinching plasma is considered as colliding particle beams, performing the targets each other. A similarity of this concept with - 3 - the ideology of inertial confinement is evident: during the "clean*1 implosion only the kinetic energy of accelerated particles increases until they reach a close surroundings of the axis and only there the plasma stagnates and therma- lizates»

The experimental research has changed from the classi­ cal Z-pinches imploding from the whole volume of discharge chamber, completely filled Ъу working gas, to other pinches with pulse injection of the gas into the vacuum chamber (gas-puff Z-pinches) [з] • The absence of gas contact with the wall enables more uniform ignition of the discharge and a minima li zat i on of impurities in plasma» Usage of a hollow gas cylinder is then more advantageous to achieve higher implosion velocity, compression and plasma temperature than in the ease of ful cylinder [4, 5>] . Shorter period of dis­ charge circuit (on order of us or hundreds ns) provides better prevention of MHD instabilities»

large experimental devices with gas-puff Z-pinches ere nowadays the most effective Impulse source of soft X-rays (the conversion of applied electric energy into X-rays achieves up to 22 % [б]) and on their basis the X-ray lasers are developed. As regards the thermonuclear research, linear Z-pinch is again studied as one of less conventional alterna­ tives of thermonuclear reactor Í7, 8 J • - 4 -

2. Experiment

At the Institute oi' Plasma Physics (Czechosl. Acad* Sci., Prague) the device of gas-puff Z-pinch was completed for experimental study of its physical properties and fur­ ther applications as an impulse soft X-ray source (calibra­ tions of X-ray detectors, X-ray lithography).

The apparatus consists of capacitor bank (10.8 oP).9 charging and switching circuits, main spark gap switch, flat low-inductance high-voltage conductors, discharge chamber (0 260 mm), pulse electromagnetic valve (with filling volume 1,2 cnrvshot) and vacuum pumping system (10""^ Pa), Working gas (Ar or Ne with initial pressure from 1 x 1CK to 7 x 1(r expands into the chamber and annular nozzle forms the hollow gas shell and directs it to the space between the electrodes (fig, 1), The filling of interelectrocle gap was measured independently by ionization gauge and by means of high voltage breakdown between the electrodes. On the basis of these measurements a proper delay between gas valve openning and main spark gap switching was selected [9J • An open-air main spark gap working in multichannel regime is triggered by this chain: time unit —» hydrogen thyratron —* coaxial trigatron spark gap —» main spark gap.

It is desirable that the pinch should occur as close as possible the current peak and maximum energy of magnetic field should transform, into the kinetic energy of particles. Considering that the current period is determined - 5 -

Ъу construction of main circuit, it is necessary to comply with this requirement by changes of other discharge parame­ ters. Working regime of our Z-pinch was consequently optimi­ zed Ъу electrodes geometry, initial gas pressure p , capaci­ tor charging voltage U and the delay between valve closure and main spark gap switching S^rp, Following initial confi­ gurations of gas cylinder were studied (length: diameter):

A. 2,5 1 (42/17 mm), B. 1 1 (21/21 mm),

С 1 2»5 (21/52 mm). The most suitable working regime in described experiment (not only from the energetic point of view, but also from point of view of discharge stability and X-ray radiation) proved to be such regine where U = -30 kV, S^p = 350 ps 5 for We (400 ps for Ar), p0 = (4 - 7) x 10 Pa, configuration B.

Particularly, the measurement of soft X-ray emission of pinch was exploited for high-temperature plasma diagnos­ tics. X-ray detection methods with temporal, spatial and spectral resolution were utilized. The X-ray diagnostic tilth temporal resolution was carried by 2 types of detectors. The vacuum X-ray diode (XRD) with an alluminium cathode for the region of ultra-soft X-rays (hv = 10 - 1000 eV) takes advantage of the photo-effect as a dominant process in the X-ray interaction with matter. The XHD is censitive neither to visible light nor to hard X-rays and makes possible the temporal resolution better than 1 ns. For the measurements - 6 -

in the region ofhv =1-10 keV, the semiconductor surface- -barrier detector (SBD) was used. In order to improve the response speed (below 10 ns) and signal-to-noise ratio, a voltage* in the reverse direction was applied to the SBD. Some filters of thicknesses <1 p (ZRD) or several Ш (SBD) and 4-channel set-up of both types of detectors were employed for a simple spectrometry. The XRD a SBD were placed in radial distances 35 - 190 cm from the axis of the discharge chamber. Other used methods of X-ray diagnostics (pinhole cameras, crystal spectrographs) are described elsewhere |_10J .

3. Results

a) Electric characteristics of the discharge

In a short-circuit connection, high-current generator is working with period T = 7*8 jusj the inductance of main circuit is 143 nH. Charging the capacitor bank up to the voltage -40 kV, we obtained the initial current rate about 2 x 10'1 A s"1. Other characteristics of the circuit are shown in table 1; Short-circuit current I_ was measured by

Rogowski colls (fig. 1)f the maximum current I was calcula­ ted for lossless LC-^ircuit. The difference between both currents is caused by the energy loss in the circuit, espe­ cially in the spark channels of the main spark gap switch*

During the discharge in gas (plasma) load, its resis­ tance and inductance are changing. The imploding cylinder - 7 - inductance rises from some nH to several tens of nH. This rapid growth of inductance at the end of implosion causes typical break (drop) of current signal (see time 9p in fig*2) which coincides with a moment of the imploded plasma shell collapse on discharge axis. On the contrary, relati­ vely big load resistance in the discharge beginning decreases rapidly with rising current, at a time t<žC9p due to avalan­ che ionization and then due to Coulomb collisions. So the resistance does not affect the discharge later. Because our Z-pinch occured before current maximum, increasing current and magnetic field at Sp < t < T/4 makes further plasma implosions possible as seen from fig. 2. « b) Dynamics characteristics of the implosion

We assume that the plasma cylinder axis is parallel to the z-axis and that only the components 32 and B^ of the current density and the magnetic induction are not equal zero, (r, 1^ and z are the cylindrical coordinates). The dynamics of Z-pinch implosion is then described by mo­ tion equation <1> V*- 9& + Ш

J where 9, p, vr are the density /kg m / , pressure and radial velocity of the gas (plasma)» respectively. Approxi­ mate solution is given by snowplow model [l1J : neglecting gae pressure it is considered a fully ionized thin layer at the cylinder surface which sweeps up the cold gas below this' layer. We simplified snowplow model by the assumption - 8 - that the mass M(t) of the accelerated plasma remains cons­ tant during the implosion of hollow cylinder. The numeri­ cal solution of non-linear differential equation

C2) dV Pol2(t)1 ^? s * 4*а(Ш with initial conditions

(3) aCt-O) = A, (ff )t=o = 0, gives the results shown in fig* 3. Here a, 1 are the cylin­ der radius and length, respectively, and the current

I(t) = Ie sin w t.

By fitting the values of the mass M we reached an agreement between calculated and measured implosion times Sp. However, we -have to take into account that this amount of accelerated mass is only some frac'tion of all mass betweet „7 the ^-strodes. This total mass is on the order of 10 ' kg (after a model of adiabatic expansion of the injected gas Into vacuum). Using the classical snowplow model with ful gas cylinder, a correction of 9p obviously is not funda­ mental; the corresponding curve in fig* 3 was calculated for M(t) = M(0) + STf 1(A2 - a2), where the initial mass M(0) = 7.5 x 10"8 kg and the gas density ^ « 10"2 kg m"3. Calculated radial velocities at discharge axis are (3*2 - 6.5) x Ю4 m s"1 in initial configurations A. and B. with pinch current 1-е 100 - 140 kAj in configuration C« with Ip « 190 kA the velocity is 1.8 x 105 m s"1. - 9 -

с) Radiative characteristics of the pinch

The visible light photographs have shown [9J that there appears pinched.plasma fibre with the diameter of about 1 mm on the discharge axis. The current break correlates with the X-ray emission of Z-pinch as demonstrated in fig. 4» In non-optimized regimes (fig* 4b), obviously the second (occasionally the third) implosion occures as mentioned above. Better temporal resolution confirmed that the pinch fibre is relatively stable during 50 - 100 ns (XRD response in fig. 5). Then some portions of this plasma bulk are under further implosion and compress into hot spots due to the sausage instability. The hot spots radiate in wide X-ray range 30 that their emission is noticable not only from filtered SBD signals (hv ЭЕ 1.5 keV) and pinhole photographs but also from an increase of XRD signals. The shapes of X-ray signals from Ar and Ne do not differ each other substantially! the amplitude of XRD signal is roughly 1/5 lower for Ne (the smaller number of radiating shell electrons corresponds with the lower electron density in Ne plasma and with the smaller number of possible recombination transitions).

Total ultra-soft X-ray output from the plasma bulk of our Ar pinch reaohed 125 J/49T during a peak with a half- -width about "200 ns| this yield corresponds to the average power 0.63 GW. In this case, the total electric energy of capacitors is converted into X-rays with the efficiency 2.6 % (considering only magnetic field energy ы|/2 actually participated in implosion, the conversion efficiency is then - 10 -

9,6 %)• Measurements with the XRD filtered by a filter of ^Z 0.5 um-thick nitrocellulose layer showed that a crucial portion of the emitted X-ray power lies below the energy hi» ^*- 100 eV. For higher energies the radiated power strongly decreases and some differences between line spectra of Ar and Ne emerge* By means of the SBD, outputs 0.23 J/43T in the region of hv 5^-400 eV and 0,007 J/4SC for ЬуЭя.5 keV during 50 ns pulse were measured for Ar pinch.

4. Discussion

For the case of implosion in preliminarily filled chamber, the empirical relation

where (dl/dt)t_0 = U /L, is valid [12] • Our data analysis confirmed an approximate validity of (4) also for the gas-

-puff Z-pinchf where M = M(pQ, 9yp)« However, our assumption of M = const, during the implosion is only first approxima­ tion, because no gas cylinder is absolutely hollow. On the other hand, it is so far open question, how long the implo­ ding plasma shell is "transparent" for neutral gas inside the shell and from what state of discharge (i.e. what plasma densities and temperatures) the plow mechanism is fully plausible.

From our measurements it is,possible to make some estimates concerning the plasma bulk properties. We assume - 11 - that, the Bennett equilibrium PI2 (5) (a, + V к > « ^5-j constitues itself on the observed 1 mm diameter of imploded fibre and the plasma inside the fibre is isothermal (T = = Tj в T) and homogeneous. The lifetime of plasma bulk until its disintegration caused by MHD instabilities is on the order of the ion transit time through the fibre in the trans­ verse direction [13]

1/2 (6) S"v Ы 2 a (2 к W" f where вц is ion mass* For Ar pinch and the time S^. — 65 ns we obtain Tj • 50 eV, Prom the relation (5) we can estimate the densities for this temperature in configuration B, (Ip * 140 kA): because a ful ionization of valency shells may be expected in the pinch [14] , the ion density is then

25 3 26 n^aí 1.7 x 10 m" and the electron density ne^ 1*4 x 10 •4

5. Conclusion

The optimization of working regime allowed remarkable Increase of the pinch current* In comparison with the initial results from this experimental device [15] » the ultra-soft X-ray emission was enlarged by more than one order• So, this X-ray source is now comparable with others of its class described elsewhere [16J although the keV-line spectra output - 12 -

does not achieve possible value so far* The properties of hot spot plasma are the object of further study [ю].

The author is riateful to P. Šunka for stimulating discussions and also to V. Piffl and J« Rauš for their help concerning X-ray detectors. - 13 -

References [ij Arcimovich L. A. et al. i.Atom. Ehergjia 1 (1956) 76. [2] Tack J. L.: In Proc. 2nd U. N. Conf. on Peaceful Uses of Atom. Energy, Geneva, 1958, Vol. 32, p. 3. [3] Shlloh J., Fisher A., Rostoker N.: Phys. Rev. Lett. 40 (1978) 515. [4] Shiloh J., Fisher A., Bar-Avraham E.: Appl. Phys. Lett, 35 (1979) 390. [5] Stallings С et al.: Appl. Phys. Lett. 35 (1979) 524. [б] Matzen M. K. et al.: J. de Phys. 47 (1986) C6 - 135 (Bit. Colloquium on X-ray Lasers, Aussois, France, 1986). [7] Unconventional Approaches to Fusion (eds. Brunelli В., Leotta G. G.), Erice, Italy, 1981. [в] Bolton H. R. et al.: in Proc. 11th Int. Conf. Plasma Phys. and Cpntr. Fusion Research, Kyoto, 1986, IAEA Vienna, 1987, Vol. Ill, p. 367. [9] Krejčí A.: Thesis, Inst. Plasma Phys., Prague, 1988. [10] Krejčí A., Krouský E., Renner 0.: to be published. [11] Pereira N. R., Davis J.: J. Appl. Phys. 64 (1988) R 1. Г12] Lukjanov S. Y.: Hot plasma and controlled thermonu­ clear fusion. Nauka, Moscow, 1975» p« 343 (in Russian). [13] Vikhrev V. V., Braginskii S. I.: in Voprosy teorii plazmy (ed. Leontovich M. A.), Vol. 10, Atomizdat, Moscow, 1980, p. 244* [14] Itarrs R. E. et al.: Appl. Phys. Lett. 42 (1983) 946. - 14 -

[15] Krejčí A*, Krouský E., Renner 0.: in Proc. 14th Czech. Seminar on Plasma Phys. and Technol., Prague, 1987, IPPCZ - 277, Part II, p. 16. [16] Bailey J. et al.: Appl. Phys. Lett. 40 (1982) 33.

/ - 15 -

Table 1

Electric properties of main circuit operated by a multichannel spark gap switch.

charging capacitor short-circuit calculated voltage UQ/kV energy E/kJ current Ie/kA current I0/kA

- 25 3.375 145 202 - 30 4.86 175 243 - 35 6.615 210 283 - 40 8.64 245 324 - 16 -

1 g. 1. Schematic cross-section of the vacuum chamber: 1 - insulator, 2 - cathode, 3 - nozzle (grounded), 4 - fast valve, 5 - annular gas jet, 6 - pumping port, 7 - Rogowski coil, 8 - diagnostic window*

Pig. 2. Measurements of dl/dt (output of a simple loop, top trace) and I (self-integrating Rogowski coil, bottom trace). The !L identifies the time of thyratron triggering.

Pig, 3. Temporal development of imploding plasma radius, velocity and magnetic field on plasma surface. Configuration B.: implosion of hollow cylinder (II = 7.5 x 10"8 kg, dashed line) and ful cylinder (for M see the text, dotted line). Configuration C.: implosion of hollow cylinder

8 (M = 2.5 x 10" kg, ful line), radial velocity vp of plasma shell ard magnetic induction B^, in radial distance a(t) from z-axis (both dashed-dotted lines, right scales).

Pig. 4. Oscillograms show a correlation between the break of discharge current (top trace), XRD signal (middle trace) and SBD signal (bottom trace): a) optimized regime in Ar with only one peak of X-rays, b) non-optimized regime in Ar with further peaks.

Pig. 5. Typical pulse shapes of XRD (upper trace) and 120 ua Be filtered SBD signals, (lower trace). - 17 -

E

m

V;.*y ;;:•;:: es

\

ílg. 1 - 18 -

ТТ О 1 Тр 2 t/jis

Pig.. 2 - 19 -

!/*•

•н

^ UOjfO|dUI| JO •}!* 20 -

>U""N^

/ "^-^-^^ 7 я" Й 3-

=Д1 = ± í

500 ns /div

b £=* 500 ni/div

Л". 4 - 21 -

í ч 100 ns /div

Pig. 5

TZ 56 ABSTRACT

The fast linear Z-pinch was experimentally investiga­ ted using a pulse high-current generator (10.8 11F, 3-10 к J, 150 - 230 kA) and a pulse injection of argon and neon* Measu­ red electrical characteristics of the discharge (current shape and rise time, inductance) and calculated dynamic para» meters of plasma implosion (accelerated mass, radial plasma velocity) are presented* X-ray diagnostice with temporal resolution (vacuum X-ray diodes, semiconductor detectors) were utilized* The temperature and the density of pinch 26 3 plasma (Te££ 50 еУ,п#л«1.4 т Ю m" ) as well as other its parameters (size, lifetime) were estimated* Total energy emitted by pinch in ultra-soft X-ray region (hv <: 1 keV) during ~ 200 ns pulse achieves 125 J/43P •