Structure of the magnetic fields in Z-pinches G. S. Sarkisov and A. S. - PDF document

Structure of the magnetic fields in Z-pinches G. S. Sarkisov and A. S. Shikanov P. N. Lebedev Physics Institute, Acadenry LPMI, Ecole Polytechnique 91128, Palaiseau, France V. V. Yan'kov Russian Scientific Center "Kurchatov 123182 Moscow, March 1995) ~ks~. Teor. Fiz. 108, 1355-1372 O 1995 Anierican Even after several decades, there is no flagging interest in Z-pinches. There reasons for energy in the constrictions makes it possible to obtain plasma extreme parameters, is exploited in applications. Second, of the constrictions is interesting physical fusion.'-3 The more recent projects have been to the c~m~ression.~-~ play an important role pulsed source neutrons?-l2 are also generate powerful the range from eV to 10 keV The corona current is promising active medium for in the rays.8 All these applications require an under- standing of the physics of the constrictions. The property of energy focusing in the constrictions of 2-pinches through the nonlinear stage m=O instability mode1' "plasma focus" devices."-"'1° To describe the self-focusing, a scaling estimate4'I7 proposed, derived from constriction and, therefore, magnetic energy ~(llr)~ during compression constriction. The constriction.18 restricted to linear electron densities: the ion At lower linear density, Alfvdn velocity, and the plasma must described, at equation gives accurate description. the Vlasov did not reveal development of constri~tion.'~ However, the Vlasov important effects MHD.~~~~-~~ this hydrodynamics (convection field by the specific resistivity) found in theoretical studies ions can was found that approximation can also for pinches N, when it of the main application experiment.8y22 The stabiliza- was based parameters,13-'4-24 and therefore it is important to measure it directly. 743 JETP 81 (4), October 1995 1063-7761/95/100743-10$10.00 O 1995 American Institute of Physics 743 ing the magnetic fields on the use Faraday magnetooptical effect, as it propagates along the the plasma. Simultaneous measurement rotation angle the plane shift makes spatial distribution magnetic field The diagnostic possible to re- spatial (about ,urn) and time (-I resolution without at the same time the plasma parameters (the probing radiation Faraday measurements is usually at the - 100 MWIC~'). The measurements are made using three-channel polarointerferometer, makes it possible observe simultaneously The method dense plasma is described in Ref. The Faraday rotation method successfully used in studies to measure the space and plasma.25-29 current systems, realized in "plasma focus" devices,30 high-current Z-pinch in the Angara-5-1 facility,31 and also in low-induction vacuum sparks.32 ever, practically all studies using have been made in the first place the purpose detection rather Sec. of the method of measuring magnetic Sec. diagnostic complex. In Sec. give the experimental results. In Sec. their theoretical the Conclusions summarize the THE METHOD MEASURING THE MAGNETIC magnetooptical effect consists an electromagnetic wave as it along the rotation angle is given wavelength in cen- path length the probing BII is the projection of the magnetic field onto the probing direction in gauss, and ne the symmetry axis plasma. It follows from the necessary to have independent information n, electron density, perform interferometry plasma simulta- The interference phase shift 6 fringes) can expressecl in the form S(y)=4.46. IO-'~X n,dl. I," (3) After the rotation angle a(y) and the 6(y) have been possible to re- the mean ki- logauss) onto the probing direction:25 As was demonstrated in 25 for Gaussian distribu- electron density, the mean the mag- netic field local magnetic same time, radial distribution the mean is identical to the distribution local magnetic The steeper the density, the smaller the difference between mean and local magnetic appreciable difference between mean and observed only the electron density toward the plasma column. an axisymmetric plasma, it possible to local distributions field and of electron density using experimentally obtained inte- grated distributions the rotation angle plane of po- larization and Let us this can be done. represent the expressions (2) and cylindrical coordinate system the form a is measured S in fringes. and (6) can readily reduced to an integral equation, the general form axi- symmetric objects Here and spatial variables scaled The analytic solution equation is known the "Abel two forms: The formal expressions (5) using the normalized vari- writing down the appropriate expres- sions for f(r) and S(y). Thus, for rotation angle (4), October 1995 Sarkisov et a/. 744 Accordingly, for the phase shift (6) we obtain Knowing the functions f,(r) and f,(r), can write down the expression for the magnetic B(r) (in gauss) in distribution of the field in plasma reduces f,(r) from the polarimetry and the function fn(r) from the Abel one of its inversions (8)-(9)]. for numerical the Abel now well fairly complete on this Ref. 33. local distributions electron density axisymmetric plasma current strength I(r), current density j(r), and the elec- tron drift velocity Vd(r). The relationship between these B(r) and n,(r) obtained from is measured in n, number per square centimeter, and per second. simultaneous investigation radial distribu- rotation of of polarization interference phase the probing laser radiation. The angle small depolarization two-channel polarimeter. This makes errors associated probing beam in the transverse gradients It is assumed that the parameters do time to probing; the sign vector onto assunied to be constant. It is assunled that the Farday mechanism of of the LIS this last assumption well known that any permittivity tensor plasma leads in the general transverse gradients electron density can also, longitudinal magnetic field, have of the data published 36 showed detecting optics is restricted -10" the wave is due Faraday effect. strong effect an increase in wide-aperture detecting optics i.e., strongly diffracted rays are detected. is because sig- the probing electromag- as a of the transverse electron density gra- also accompanied DESCRIPTION OF The experiments current generator (Ecole Polytechnique) with the current strength kA, pulse -50 ns, power TW. For probing the Nd:YAG (QUANTEL NG-24) was consisted of 3-nanosecond generator and three amplifiers. wavelength 1.064 pm was =I After nonlinear frequency doubling parameters: wavelength pm, pulse duration -3 ns, energy -250 mJ. The ac- with the GAEL ?5 optical arrangement of the which made and record shadow, and interference images of the spatial resolution pm and time resolution -3 time resolution de- pends on pulse duration polarointerferometer). For the polar- Glan prisms with aper- ture 20x20 mm2 were used. The polarimeter contrast 5. lops, the plane polarization to The difference of the was less For coordinate three images, visualizing stop the plane then the of the plasma together with the the Faraday film polar- izer, a 3" wedge made an exit The calcite angle. Thus, two images radial direction are The exit polarizer interferometer, two beams (4), October '1995 Sarkisov et a/. 745 FIG. 1. three- polarointerferometer: I-GAEL 13--Gl,u1 prisms; 4-plasma; 5, &lenses; &spatial 7-visualizing stop; 162" glass wedge; 11-100% Al mirror; 12-shift polarization interferometer (entrance polarizer-3' wedge-exit polarizer); 14, 15, lbCCD ference channels. in the region in which they are superim- equidistant interference fringes are formed. a number polarizer makes to equalize interfering beams. reduce the frequency filtering. In front narrow-band inter- ference filter, lens 5 a stop The slit to the of the stop laser radiation had not undergone refraction refraction perpendicular which the sity were same time, the radiation itself did not have not focused this caused the stop to As photodetectors, three CCD (Philips NXA 1050/50). developed a spe- cial electronic distributor to ensure synchronization with the The signals from to the memory of individual controller cards PC-286 personal then transferred format. Before the CCD in the a 9-step neutral optical at- written for rotation angle the magnetic field tron density, plasma parameters. The rota- tion angle of the was recovered relative intensities and shadow channels. The accuracy in rotation angle -0.1'. were largely uncorrelated interference Faraday and shadow channels associated the high degree laser radiation. The method was to recover interference fringes corresponding sections of unperturbed (obtained directly device) interferograms compared. In an ap- proach, the accuracy in the phase rotation angle and were then smoothed and to construct local distributions the magnetic field, current strength, current density, plasma parameters. an analy- plasma yields two-dimensional distribution of the plasma parameters. THE EXPERIMENT used thin different materials (Al, diameter 20-25 Faraday (a), shadow (h), ;lnd interfcrcncc (c) images of plasma formed by the explosion of ;I 25- micron A1 wire. Thc image was obtained 55 ns al'lcr the beginning of thr current and 13 ns hc(i)rc the heginn~ng of Ihe x-ray emission. The cul.rcnt strcnglh ;I( the proh- ing time was - 100 LA. 746 JETP 81 (4), October 1995 Sarkisov et a/. 746 R. pm interference phase magnetic field induction (curve 1) and region of the constriction (a) density (curve pm a set placed behind different filters, investigated the time the x-ray each firing of the measured the time profile placed in a return the probing laser radia- pinch plasma a high-speed characteristic values the ro- the plane and of the interference phase of the were -0.5" and -27r, 2 shows and inter- ference (c) images the plasma produced 25-micron aluminum probing was the current 40 ns for of the induction sensor, the kA. In the can see a well-developed constriction appreciable Faraday the plasma plumes, but our attention the region pm. The distributions of the are shown pm from the kG (corresponding to a current kA). The electron has a =5. 1018 opacity boundary distance -280 pm then rapidly Figure 4 shows the interference (a) and of the rotation angle directly corresponds of the (see Fig. was pos- measure reliably the at the of -0.3 of a fringe to an electron den- -5- 1018 at -50 pm from the the rotation angle of the tion clearly has -0.05". The reliable the phase -0.05 of upper bound pm of the pinch of the B kG, responds to a current 1 kA. the pinch same time, 5b (a fragment shadow image a slight can be observed in the region immediately next to the same position in the interferogram, one can see small disturbance 6 fringes a 0.3 0. lo0 0.05O 0.2 FIG. 4. Radial distribution of the inter- 0 ferencc the rotation the plane (b) in section b identified in Fig. 2. -0.05" 0 -0.10" 0 200 100 600 500 1000 1200 1100 0 200 100 600 SO0 1000 1200 1400 747 JETP 81 (4), October 1995 Sarkisov et a/. 747 the pinch. density the Despite the appre- Figure 5a shows two-dimensional distribution ciable errors the measurements, the presence shift recovered sec- the magnetic pm from the center of tions in the interferogram at intervals of 25 pm. is an experimental fact and by the image that constriction forms in this region the measured rotation angle the periphery of has a maximum while similar picture was observed ference phase shift has many firings constriction could be detected. the magnetic field at the boundary of the plasma plumes Faraday (a), shadow (b), and inter- the plasma the explosion The probing was done ns after and -17 ns of the current strength at this time was -190 kA. In the Faraday image, it can seen that is an appreciable magnetooptical effect the region the plasma plumes, which radial distribution the magnetic electron density in section in the plasma plumes. was observed to rise rap- and then The electron density also increased to -2.1. 1019 cm-3 and then decayed. interesting to the region in electron density has the region maximum of the electron FIG. 7. R;rdial distribution of the magnetic lield induction (curve I) and of rhc clcctron density (curve 2) in section tr identilied in Fig. 6. now consider the magnetic field at shows the Faraday (a), of the the explosion The probing ns after the current =40 x-ray emission. The current this time was approximately kA. this shot, =O not yet it proved to be the boundary (and not plasma plumes, as Fig. 6). radial distributions the magnetic electron density in section magnetic field induction reaches kG at -410 pm pinch and then decays. electron density decreases from the value -3. 1019 cm-3 the boundary of the opaque region (-340 pm ter) toward the periphery of result is the that magnetic decreases radially " the peripheral the Z-pinch. Figure shows the radial of the current strength and the current density The current reaches =60 kA at -410 pm from the center within 20% with the the electrotechnical current density has maximum of MAIC~~ rapidly and this region of detectable values of the the plane cloes there is (4), October 1995 Sarkisov et a/. 748 FIG. 8 Faraday (a), \hadow (b), and ~nterfercncc (c) Images of the plasma tormed by cxplos~on of 20-m~cron Ta wirc. The Im,lge w,~s obta~ncd 30 ns alicr ~hc begln nlng ot the current and 40 ns betore thc bcgtnnlng of the x-ray cmisslon. Thc current strength at the tlmc of problng was -55 DISCUSSION OF THE RESULTS the pinch most remarkable from the constriction (the current through the 2% of total current through the pinch). Such standard one-fluid scenario. Analytical tions describing restriction to near the completely clear. can be The description is simplest one ignores and the netic field is frozen just the shall assume that electron linea to the applicability (1) corresponding in our to the have here doubly ionized aluminum. In the interference meas~rements,3~ constriction is close to loL5 cm-', the region consider a stationary axisymmetric force lines field with small cross section Then conservation of the BS= const. (15) When the the electron current to a tube is conserved: ZmBr= const, (16) distance to law that the ions corresponds to corresponds to quasineutrality to conservation given magnetic 2.rrrSne = const (17) Eliminating S the three (15)-(17), current flows along I= 1(n,r2). (18) This simple important result obtained in the plasma and in was derived from the conservation laws, under which ion- acoustic resistance, ion current, of the constriction. The (18) there (4), October 1995 B. k~ v om3 I, k~ J. MA/C~* Sarkisov et a/. 749 - - - - - 80 60 60 -3 40 40 20 20 Radial distribution lnductron (I) and of thc clcctron dcn- -2 0 0 sity (2) (a), and also of the current strength -20 -20 (1') and of the current density (2') (b) in the I -40 40 section (I 300 350 400 450 500 550 350 400 450 500 550 this contradicts an plasma along constrictions, as conjectured that the constrictions cease they reach the MHD.~~ more physical form, this important the order constriction at values does ent types pinch; moreover, the constrictions survive stabilized state for 100 MHD-times (see 8). In our experiment, electron linea density was initially current velocity electrons was not with the Alfvdn velocity, and therefore the scenario described above ever, the the current from the constriction can stated at once: Since electron linea density in the constriction, the current will displaced from the expression after this question arises. no current in did the constriction arise? c~rrent,2~'~~ tacitly assumed that such must not arise. explain our experiments, to consider experience gained near relations s~itches~~-~~ is helpful. The opening switches of two coaxial cylinders, gap between which is plasma. They possess axial like Z-pinches, is an explosive growth of resistivity, though the subsequent evolution is the opening switches, the current transferred along coaxial channel to the useful load, but pinches there current to continues to possible displacement opening switch is inner part therefore com- the current to the axis is forbidden but the resistivity nevertheless occurs for some phenomenon was to peak the power experiment^.^^^' the reason for current breaking, growth of the vacuum gap near suggested; direct experimental information opening mechanism was not available. Reference effect on the basis that was originally devel- pinches.8s20*2' represent this re- (in ohms) form23942 where u = ll(.rrr2n,e) is the the mean current ve- resistance corresponds UB~IX rr, the lan- the loss p=eA/c, tor potential (19), of the linea density causes the plasma rise long before the occurs at the linea density gives to heating the plasma growth of the opening switches electron MHD found confirmation Ref. 43, and later theory were made Ref. 45. constrictions under the conditions linea density, sufficient to the theory opening switches Ref. 45, however, the possibility strong change of the practice to replacement the expres- sion "density" the expression "linea Thus, the constriction develops growth of the magnetic pressure due to compression, as ordinary pinches of high of the electrical resistance current is transferred to the pinch interesting feature observation at the plasma plumes magnetic fields pressure ex- an order pressure corresponding the total For this, several explanations. For example, symmetry is lost, the standard procedure for recov- local plasma parameters can lead to overestimated results. However, analysis does not this hypothesis. Another is associated the magnetic field by these must ultrastrong shock waves, The most natural one well laser plasma, namely, the nonparallel gradients the temperature (thermoelectric power mechanism). the nonlinearity to the dissipation are ignored, generation equation has the simple dB -- Vn, - 1 OOVT, -, at n, where B is measured in megagauss, the distance in centime- ters, T, electron volts. For our conditions, taking gradients, characteristic distance -50 pm, time - ns, and -25 eV, we obtain a field - while the field is is the radial profile B(r) in Fig. 71. course, for energy density and therefore that the (4), October 1995 Sarkisov et a/. 750 FIG. 10. Distributions of the parameters n,r2 (I) and Br (2) constructed for the radial electron density n,(r) field induction B(r) shown in Fig. 7(a) and in Fig. 3(b). next to constriction. This sistance; third, there is motion the much dense plasma of the the electron our experiments, unam- biguously say which of factors is most important. the boundary 2-pinch in Fig. 8) strong reverse pinches,46 also appear entirely naturally in the which may have been observed make possible law in MHD. In (18), possibility is current along passes through twice, ex- pression (18) can Let us consider electron density the plasma and the magnetic field shown 10a corresponding to ne(r) and B(r) The extrema good accuracy. lob corresponding to case, coincidence extrema (but "out is observed. can be seen equal values linear density probable that moving along the axis the pinch, turn round investigated section second time. streamlines turn leads to channel and, accordingly, llr) decay of the magnetic field at the boundary of the 2-pinch. Thus, the dependence (18), fundamental for has been time. neither case branches observed. of the rotation angle and the interference shift that can factors also cause tielcl nonparallel tempera- ture and density gradients; second, there is the electrical re- Our measurements of the netic fields in to discover constrictions. This our operating in the linear electron densi- ties. Despite the small radius of the pinch experiment to observe (for probing at X=532 phase shift. These effects admit The effect current loss from the constriction (according the total the pinch it) can explained by convective transfer and the of the in plasma opening switches. multaneous measurements spatial distribution field induction and of density made the range linear densities the first time the law (18) used in many theoretical preliminary result. Nevertheless, it hoped that subsequent experiments Faraday diagnostics the pinch it possible two-dimensional pattern of the is difficult to overestimate measurements for the theory have actually found plasma parameters that is same time differs appreciably from ordinary The fragmentary detection Far- aday magnetooptical 2-pinches that the sensitive at the wavelength nm, and the infrared wavelength range. may be that further 2-pinches. 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