Measurement of the polarization of line profiles in the X-ray region and the diagnostic possibilities

Pergamon PII:

J. Quant. Spectrosc. Radiar Transfer Vol. 58. No 4-6, pp 531-536. 1997 0 1997 Published by Elsewer Science Ltd. All rights reserved Printed m Great Braam 0022-4073/97 $17 00 + 0.00 SOO22-4073(97)00059-9

MEASUREMENT OF THE POLARIZATION OF LINE PROFILES IN THE X-RAY REGION AND THE DIAGNOSTIC POSSIBILITIES E. J. CLOTHIAUX,

E. OKS, J. WEINHEIMER,

V. SVIDZINSKI

and A. SCHULZ Physics Department, Auburn Umverslty, Auburn, AL 36849-5311, U.S.A. Abstract-A relatively new technique for polarization analysis of X-ray line profiles was employed. A significant difference in profiles of the Al XII Lyman y line registered in two orthogonal linear polarizations was observed in a powerful Z-pinch. This is a measurement of a polarization of X-ray line profiles in laboratory plasmas. The observed polarization of the profiles was interpreted as being due to strong Langmuir waves developed primarily along the discharge current. This diagnostic technique could also be applied to other areas of high-temperature plasma research, for example, to laser fusion. It may be the first measurement of polarization using the profiles of X-ray lines. 0 1997 Published by Elsevier Science Ltd. All rights reserved

1. INTRODUCTION

of profiles of visible spectral lines are widely used for diagnostics of waves in low- and medium-density plasmas by the appearance of anomalous electric fields (AEFs) - see, e.g., Ref. ‘. The theoretical idea behind these diagnostics is that AEFs frequently develop anisotropically, leading to a linear polarization of AEF-broadened line profiles. The main advantage of this method is that the “isotropic” broadening mechanisms, such as Doppler, instrumental, opacity, and “normal” Stark broadenings, do not contribute to the linear polarization of line profiles and are effectively removed from the competition with manifestations of AEFs. We present here the first measurements ever of a polarization of X-ray line profiles in a laboratory plasma. The experimental design of the X-ray polarization measurements is based on the following: if one observes a spectral line employing a crystal at the Bragg angle, and then observes the same line after rotating the crystal through 90”, the resulting spectra will correspond to two orthogonal linear polarizations. This can be achieved by using two spectrometers, so positioned with respect to each other that the plasma line source is in the plane of the spectrometer in one case and perpendicular to it in the other case (Fig. 1). Measurements

of a polarization

2. ANALYSIS

OF THE

EXPERIMENTAL

DATA

We have successfully implemented this design in experiments at the advanced plasma radiation source PHOENIX 2. PHOENIX is a powerful Z-pinch in which the current reaches peak values of several megaamperes during several tens of nanoseconds. We have employed two high-resolution, X-ray crystal spectrometers to record time-integrated profiles of the L, and L, lines of Al XIII observed in two orthogonal linear polarizations: one polarization parallel to the discharge current, the other perpendicular to it (Fig. 1). In the red wing of the L, line and in the blue wing of the L, line we have observed blending lines of Al XII and/or Al XIII as well as Si XIII. Fortunately, we have been able to analyze in detail the shape of the blue wing of the L, line and the red wing of the L, line as they were free from blending lines. For the experimental identification of the relevant line broadening mechanisms, the L, line is more appropriate than the L, line, as the former does not have the central (unshifted) Stark component that would modify the intensity trend in the spectral region around the line center. If the primary broadening mechanism were the normal Stark broadening by ion and electron microfields, then the wings of the L, line should demonstrate a power law Z(An)cc(Al) -q, where 531

532

E. J. Clothiaux et al

I II I- II r-

II

l-t#l\

,(lUU)

x-raysource ’

(2d = 8SlA) /

L/Ah>3500

-

I

/ a

‘------film/^

Fig. I. Scheme for experimental analysis of a linear polarization of X-ray line profiles.

2 I q I 2.5. In this situation the logarithm of the experimental profile intensity versus the logarithm of wavelengths would approximate a straight line of slope q for most of the profile. However, Fig. 2 clearly demonstrates that this is not the case for our experimental profiles. On the other hand, if the primary broadening mechanism were Doppler broadening, then the value of log[Z(AA)/Z(O)]should be proportional to (An) 2. In this situation the plot of the experimental values of log[Z(Al)/Z(O)] versus (Al) 2 would approximate a straight line. However, our experimental profiles are not straight in these coordinates either. In contrast, we find that the experimental profiles of the L, line are approximately straight lines when plotted as log[Z(AA)/Z(O)]versus (An), as demonstrated in Fig. 3. This “log-quasilinear” shape of hydrogenic lines is well known for Balmer lines observed in solar flares where it is considered as the manifestation of non-thermal processes in the solar plasma and of AEFs that accompany those processes 3-5. While a variety of AEFs had been spectroscopically diagnosed in plasmas of electron densities N, I 1020cm -3, for high-density plasmas of N, > > 1020cm - 3, expected at the final compression stage at PHOENIX, all the types of AEFs, except those associated with the Langmuir waves at the plasma electron frequency o,, would be strongly damped due to a high collision frequency ye. Indeed, using the standard formulas of plasma physics 6, one can estimate that, for these high densities, only the Langmuir waves have a frequency significantly higher than the coliisional damping rate ye.

1119 '1

IO Parallel

100

,:--fy" 1

100 Perper$qC"li?4~

Fig. 2. Experimental profiles of the AI XIII L, line (6.053 A) recorded in two orthogonal linear polarizations in shots 1119-I 122. The profiles are plotted in Log-Log coordinates. Readings at each abscissa axis are given in mA.

Measurement

of the polarzation

of hne profiles

in the X-ray

region

533

1

ok-

1122 0.1

omIG” (I: EL0

1

112l

0.1

50

100

‘h

1119

0.1 t-++

,:
100

Parallel Fig. 3. Same as in Fig. 2 but plotted

50

100

Perpendicular as Log I vs. AA.

The formation of logquasilinear profiles of hydrogenic lines due to the AEFs at the frequency o, can be explained as follows. It is well-known that under the action of the multi-mode AEF at the frequency w,, the profile Z,(Ao) of a lateral component number k splits up into equidistant satellites at frequencies Aw = + pw,, where p = 0, 1, 2.. (see, e.g., Ref. ‘). The envelope of the satellites of one lateral component is a Gaussian (Fig. 4). The width of the Gaussian is (Aw),, = C,E,, where C, is a generalized Stark constant of the component number k and E,, is the amplitude of the AEF ‘. However, each hydrogenic line (except for the L,) has several lateral components symmetrically displaced from the line center. The contribution of each component to the complete profile of the line is a Gaussian with a width that differs from one component to another. Therefore the resulting profile of the spectral line, being the sum of Gaussians of different widths, should fall off slower than any of the constituent Gaussians. Particularly, the L, line has two lateral components and Fig. 5 shows the satellite envelopes (Gaussians) due to each of the two components and the resulting profile (the upper curve). Obviously, the resulting profile falls off slower than any of the constituent Gaussians. It turns out that for a relatively broad range of plasma and AEF parameters, the resulting theoretical profile demonstrates the logquasilinear behavior. For example, Fig. 6 shows a typical experimental profile of the L, line plotted in Log Z versus AI coordinates (dotted line) and a theoretical fit calculated as described above (solid line). In Fig. 6 the Doppler, opacity, and normal Stark effects are also incorporated in the calculations as secondary broadening mechanisms. It is seen that the theoretical profile broadened primarily by the AEFs is indeed logquasilinear and fits very well the experimental profile.

0.06

.a E

0.04

z

0.02

0.00

Fig. 4. Calculated splitting of a lateral component of a hydrogenic line mto satellites under the actlon of an electric field E(r) = Z,&cos(o,t + &). The envelope of the satellites is a Gaussian.

534

E. J. Clothiaux et al

-150

-100

-50

0

50

loo

150

w-4

Fig. 5. Envelopes of the satellites for two lateral components of the L, line under the same conditions as m Fig. 4 (dashed and dotted lines). The solid curve is the resulting profile of the L, line.

For the polarization analysis the L, line is more appropriate than the L, line, since the former is more sensitive to the electric fields than the latter. Figure 7 shows experimental profiles of the L, line recorded in two orthogonal linear polarizations (parallel and perpendicular to the discharge current), demonstrating significant polarization in the wings. We have also used a flat-crystal spectrometer that registered unpolarized profiles of the L,, Lg, and L, lines of Al XIII in a single shot. Figure 8 shows an example of this experimental data (solid lines) as well as the theoretical fit using the above approach (dotted lines). 3. DIAGNOSTIC

RESULTS

Our detailed analysis of all profiles of the L,, L,, Lg, and L, lines of Al XIII obtained during our experimental campaign at the PHOENIX, including the analysis of the anomalous intensity trend in the wings and the polarization analysis, lead to the following conclusions. The compressed PHOENIX plasma is characterized by the electron density N, N 3 x 102’cmM3, obtained from the frequency ape deduced from the primary contribution of the AEF-broadening, and by the rms nonthermal velocity of the macroscopic motion u,, N 5 x 10’ cm/s, obtained from the contribution of one of the secondary mechanisms (nonthermal Doppler broadening). In this plasma there have developed highly suprathermal Langmuir waves of the electric field amplitude E,, N 7 GV/cm obtained from the primary contribution of the AEF-broadening. The angular distribution of the field is represented by an ellipsoid, which is prolate along the discharge current, so that the ratio of its axes is approximately 3:l. This field anisotropy leads to the significant polarization of the L, line profiles. The shape of the angular distribution of the Langmuir waves is consistent with the hypothesis that the mechanism generating them is electron beams, i.e., run-away electrons, travelling parallel to the bulk plasma current.

-Theoretical

0

25

50

75

100

125

150

u.(mA)

Fig. 6. Typical experimental profile of the Al XIII La line plotted as Log I vs. AI (dots). The theoretical curve includes the action of an electric field E(r) = Zr&cos(~,t + &) as the primary broadening mechanism and the Doppler, opacity, and normal Stark effects as the secondary broadening mechanisms.

Measurement

of the polarization

of line profiles

m the X-ray

region

535

* - - - - - Parallel -Perpendicular

0

25

50

100

75 Ah(

125

150

mA)

Fig. 7. Experimental profiles of the Al XIII L, line (5.739 A) recorded in two linear polarizations: parallel to the discharge current (line with dots) and perpendicular to the discharge current (line with squares).

1.2

x C * : C

1.0

- ~ -

0.8

-

0.6

-

0.4

-

0.2

-

0.0 5460

Y

Experimental Theoretical 6

1’1’ 5520

I 5560

5640

‘I 5700

I

I’

I

5760

5620

h(mA) Fig.

8. Experimental

spectrometer

unpolarized profiles of the L,, L,, and L, lines of Al XIII recorded using a flat-crystal (solid hnes). Theoretical fit calculated as Indicated in the caption to Fig. 6 is shown by dotted lines).

The conclusion that the Langmuir waves are suprathermal is based on calculating the ratio of the measured field amplitude E,, to the theoretical thermal wave field amplitude EoT calculated along the lines of Eq. (54) of Ref. ’ at the expected temperature T - 1 keV. The calculation yields &I& = 100. We have also compared the measured field amplitude E. with the typical ion microfield F. = 2.6Z,“3eN,Z’3,where Z, is the ion charge, and obtained E,,/Fo w 40. In addition, we have compared the measured energy density E$(l6rc) of the Langmuir waves with the thermal (N,T) and kinetic (K = 3N,z&/2) energy densities of the plasma. The first ratio E,2/(16xN,T) - 1 indicates that we are dealing with a strong Langmuir “turbulence”. However, it should be emphasized that both the Langmuir waves energy and the thermal energy of the plasma are driven by the kinetic (nonthermal) energy of the compression. The second ratio E;/( 16xK) - 10m2 clearly demonstrates that only a very small fraction of the driving energy is converted into the Langmuir waves energy. Thus, our measured value of E. - 7 GV/cm does not affect the macroscopic energy balance. Note that if one assumes that the po!arization (about 50% at the detuning A1 E 55 mA and close to 100% at the detuning A1 2 110 mA) of the L, line profiles is due to the Zeeman effect, rather than due to the AEFs, we would have arrived at the value of the induced magnetic field of - 2 GG. However, the ratio of the magnetic to kinetic energy densities would have been B2(8M) - 1O+2> > 1, in violation of the energy balance, and is inconsistent. 4.

CONCLUSIONS

In summary, we have employed a novel technique for polarization analysis of X-ray line profiles. We have observed a significant difference in profiles of the Al XIII L, line measured in two

536

E. J. Clothiaux et al

orthogonal linear polarizations in a powerful Z-pinch. To the best of our knowledge, these are the first measurements ever of a polarization of X-ray line profiles in laboratory plasmas. We have interpreted the observed polarization of the profiles as being due to strong Langmuir waves developed primarily along the discharge current. These novel diagnostic results should assist the ongoing development of models describing advanced plasma radiation sources and thus result in an improved performance of the next generation of the devices. Of course this diagnostic technique could be applied to other areas of high-temperature plasma research, e.g., to inertial confinement fusion (ICF) plasmas. Indeed, it is well known that ICF plasmas are susceptible to laser-driven parametric instabilities resulting in an undesirable loss of energy 8.9. In an experiment carried out at the 24-beam OMEGA laser, a decay of an electromagnetic wave (i.e., an incident laser beam) into a Langmuir wave and an ion-acoustic wave near the surface of the critical density N, was observed using collective Thomson scattering lo. In a more recent experiment performed in the United Kingdom at a short-pulse KrF laser system “, a suprathermal level of Langmuir waves was measured in the core plasma of densities N > > N, by observing a plasma-induced satellite of an Al XII line. The origin of those Langmuir waves was attributed to fast electrons that were generated at the surface of critical density in the process of resonance absorption of the laser light and then propagated into the core plasma. Investigation of the scaling and control of the above instabilities is one of the primary objectives of the ICF experiments. Deviations from an ideal isotropy of the implosion ‘*.l3may cause the Langmuir waves to develop anisotropically, which should lead to a linear polarization of X-ray line profiles. An experimental detection of some anisotropy of the Langmuir waves would definitely mean a breakdown, at least partial, of the spherical symmetry of the implosion. Therefore the novel diagnostic technique presented in this paper seems to be also the best way to attack both the problem of the instabilities and the problem of the undesirable implosion anisotropy in the ICF experiments. Acknowledgements-The authors would like to thank J. Davis for his interest to the project and A. V. Demura for his help at the preliminary stage. This project is sponsored by the Defense Special Weapons Agency. The views expressed here are those of the authors and do not reflect the official policy or position of the Department of Defense or the US Government.

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