Investigation of the Compression of Magnetized Plasma and Magnetic Flux

Summary

This doctoral thesis investigates fundamental phenomena occurring during the compression of magnetized plasma and magnetic flux using a Z-pinch configuration with a pre-embedded axial magnetic field. Utilizing advanced non-invasive spectroscopic diagnostics based on the polarization properties of Zeeman splitting and laser-generated dopants, the research provides the first simultaneous measurements of compressed axial and self-generated azimuthal magnetic fields. The findings demonstrate unexpected current redistribution to peripheral low-density plasma, axial gradients in magnetic field distribution near electrodes, and the mitigating effects of axial magnetic fields on magneto-Rayleigh-Taylor instabilities.

Front Matter & Title Pages

Springer Theses Recognizing Outstanding Ph.D. Research

Dimitry Mikitchuk

Investigation of the Compression of Magnetized Plasma and Magnetic Flux

Doctoral Thesis accepted by the Weizmann Institute of Science, Rehovot, Israel

Author: Dr. Dimitry Mikitchuk, Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel Supervisor: Prof. Yitzhak Maron, Faculty of Physics, Weizmann Institute of Science, Rehovot, Israel

ISSN 2190-5053 | ISSN 2190-5061 (electronic) ISBN 978-3-030-20854-7 | ISBN 978-3-030-20855-4 (eBook) https://doi.org/10.1007/978-3-030-20855-4 © Springer Nature Switzerland AG 2019

Supervisor’s Foreword

It is my pleasure to introduce Dr. Dimitry Mikitchuk’s Ph.D. research for publication in the Springer Thesis series. Dr. Mikitchuk was awarded his Ph.D. from the Weizmann Institute of Science in January 2017 for the research presented in this book. The main subject of his experimental study is the investigation of the compression of magnetized plasma and magnetic field by plasma implosion. This subject is relevant to the Magnetized Liner Inertial Fusion and likely to astrophysical plasmas, such as sunspots or other astrophysical objects where the magnetic flux is frozen in an imploding plasma. Here, the magnetized plasma and magnetic flux compression are achieved by using a Z-pinch configuration with preembedded axial magnetic field. A pulsed axial current is driven through the plasma column generating an azimuthal magnetic field that through the Lorentz force compresses the magnetized plasma and the magnetic flux. The diagnostics of the magnetic fields are performed using a noninvasive spectroscopic technique based on the polarization properties of the Zeeman components of different atomic (or ionic) transitions, which enhances the sensitivity of the measurement. In his Ph.D. research, Dr. Mikitchuk made a highly important contribution to the understanding of the physics involved in magnetized plasma compression by the successful determination of the magnetic-field and current-density distributions in the non-equilibrium, transient plasmas. Specifically, his measurements include: (i) Development and implementation of localized magnetic-field spectroscopic diagnostics for pulsed-power systems based on the polarization properties of the Zeeman effect and using dopant species introduced by laser ablation. (ii) Direct measurement, for the first time, of the compressed axial magnetic field evolution and distribution during the implosion and stagnation in a Z-pinch with preembedded axial magnetic field utilizing noninvasive spectroscopic methods. (iii) Simultaneous measurement of the axial and azimuthal magnetic fields revealing unexpected results of the current distribution and the nature of the pressure balance of the axial and azimuthal fields. (iv) Investigation and demonstration of the mitigating effects of preembedded axial magnetic fields on magneto-Rayleigh-Taylor instabilities in Z-pinch implosions, using interferometric and imaging methods.

These measurements are basic and essential for the advancement of the understanding of complex plasma systems, both in laboratory and in nature. Since the magnetic field is a key factor in magneto-hydrodynamics modeling, the results are highly important for examining simulations, as well as for designing plasma configurations that are particularly relevant to the presently central Magnetized Liner Inertial Fusion approach.

Rehovot, Israel, January 2019 Prof. Yitzhak Maron

Abstract

In this research, I investigated fundamental phenomena occurring as magnetic-field flux and magnetized plasma are compressed by applied azimuthal magnetic fields. This subject is relevant to numerous studies in laboratory and space plasmas. Recently, it has gained particular interest due to the advances in producing plasmas of high temperature and density in experiments based on the approach of magnetized plasma compression [1]. Many in the plasma physics community consider this approach to be the most promising for achieving controlled nuclear fusion. To advance this approach, it is essential to study experimentally the governing physical mechanisms that take place during the compression. Performing the required systematic experiments is impractical in large-scale facilities designed for fusion demonstration.

In our experiment, we employ a cylindrical (Z-pinch) configuration, in which a current (300 kA, rise time 1.6 μs) driven through a cylindrical plasma causes implosion of the plasma under the self-generated azimuthal magnetic fields (B_theta). However, our cylindrical plasma is initially embedded in an axial magnetic field B_z. The field is quasi-statically applied prior to the high-current discharge, with a value of 0.4 T.

Here, for the first time in these researches, Zeeman-splitting observations are used to measure the evolution and spatial distribution of B_z and B_theta during the implosion and stagnation stages. The two fields are measured simultaneously, which is rather important due to the irreproducibility that characterizes such experiments of high-current pulses. The difficulties in these measurements are due to (1) the high electron densities in the plasma giving rise to large Stark broadening that smears out the Zeeman pattern, (2) the difficulty in distinguishing between B_z and B_theta, and (3) the absence of light emission from the center of the plasma column. Indeed, in previous studies, under similar conditions, the B-fields were only indirectly estimated from the plasma radius. These challenges were achieved by employing a novel spectroscopic technique based on the polarization properties of Zeeman split emission, combined with a laser-generated doping technique that provided mm-scale spatial resolution.

Systematic measurements were performed for different initial conditions of B_z and gas loads. The measurements showed that estimates of the B-fields based on the plasma radius are subjected to large errors and thus unreliable. Indeed, the simultaneously measured B_z and B_theta, together with the plasma radius and the discharge current, showed that the application of an initial B_z has a dramatic effect on the current distribution in the plasma. While without B_z the entire current is found, as expected, to flow through the imploding plasma, when an initial B_z is applied, the measured B_theta (through nabla x B = mu_0 j) showed that only a small part of the current flows within the outer radius of the imploding plasma. Specifically, when B_z0 = 0.4 T, the value of B_theta in the imploding plasma shell remains nearly constant (between 1.5 and 2 T) during the implosion, even though the current rises and the plasma radius drops. This finding indicates that for implosions with B_z0 > 0 large fraction of the current flows in the peripheral plasma residing at radii larger than the imploding plasma radius. A theoretical model, based on the development of a force-free current configuration in the peripheral plasma, is suggested to explain this unexpected phenomenon. To rigorously test this model, self-consistent 3D MHD simulations are required.

In addition to these results, the measurements provide much information useful for the understanding of the B_z-embedded plasma implosion. We measure at stagnation a ~15x compression of the initial axial B-field. This compression factor, together with the observed plasma radius, allows for obtaining the B_z confinement efficiency, which is found to be ~50%. This information is useful for testing MHD codes. Another phenomenon observed is an axial gradient of B_z in which its magnitude increases by a factor of 2 from the anode (low B_z) to the middle of the plasma column (z ~ 5 mm, high B_z). This measurement demonstrates the existence of a transition region from the uncompressed B_z = B_z(t = 0) inside the electrodes to the compressed B_z farther away from the electrode surface.

The spectroscopic measurements were complemented by 2D images of the plasma self-emission and by interferometric images. These measurements were important both for obtaining the B-field evolution and for the study of the dependence of instabilities on the different initial conditions. The measurements clearly showed the mitigation effect of B_z on the magneto-Rayleigh-Taylor instabilities.

The 2D images have also shown the existence of axially directed, filament-like regions that have significantly higher emission than the surrounding plasma. These filaments were found to be plasma regions with higher electron density (by 10–20%), and slightly lower electron temperature (by a few percent) than of the surrounding plasma.

Acknowledgements

I would like to thank people from the Plasma Laboratory of the Weizmann Institute of Science that helped and supported me during the course of my Ph.D. research: My supervisor Prof. Yitzhak Maron… Dr. Ramy Doron… Dr. Eyal Kroupp… Pesach Meiri… All the technicians in the physics department workshop, and especially Yehuda Asher… Dr. Evgeny Stambulchik, Dr. Alexander Starobinets, Dr. Vladimir Bernshtam, Dr. Yuri Kuzminikh, Dr. Subir Biswas, and Dr. Yuri Zarnizki… Prof. Amnon Fruchtman and Dr. Henry Strauss… Prof. Amnon Fisher… Dr. Marko Cvejic… Last but not least, I would like to thank my family, especially my wife, colleague Christine Stollberg… Furthermore, I want to thank our recently born daughter Yael Stollberg.

Contents

1 Introduction (1) 1.1 Motivation (1) 1.2 Z-Pinch Principle and Practical Considerations (3) 1.2.1 Magneto-Hydrodynamic Description of Z-Pinch Dynamics (6) 1.2.2 Ideal MHD Model (10) 1.2.3 Snow-Plow Model (12) 1.3 Spectroscopic Diagnostics of Plasma (17) 1.3.1 Determination of Plasma Parameters (24) 1.3.2 Determination of Magnetic Field (28) References (33) 2 Experimental Setup (37) 2.1 Diagnostic Setups (39) 2.2 Initial Conditions Characterization (43) 2.2.1 Initial Gas Distribution and Time-Evolution Measurements (43) 2.2.2 B-Dot Calibration for Discharge Current Measurements (46) 2.2.3 Initial Axial Magnetic-Field Evolution Measurements (49) 3 Results (51) 3.1 Simultaneous Measurements of the Azimuthal and Axial Magnetic Fields (51) 3.2 Axial Magnetic Field Distribution Along z-axis (59) 3.3 Effects of Axial Magnetic Field on the Plasma Implosion (61) 3.3.1 Investigation of Magneto-Rayleigh-Taylor Instabilities (64) 3.3.2 Investigation of Filament-Like Structures in Implosions with Axial Magnetic Field (67) References (72) 4 Discussion (73) References (79) 5 Conclusions (81) References (83) Appendix (85)

Chapter 1: Introduction

1.1 Motivation: The evolution of a magnetic field embedded in a conducting fluid is closely linked to the fluid motion due to flux freezing. Magnetized plasmas in laboratory settings (such as Z-pinches, Tokamaks, and plasma thrusters) and astrophysical systems display complex coupled plasma-field dynamics. Compression of magnetized plasma has received high interest for controlled thermonuclear fusion (e.g., MagLIF). A laboratory Z-pinch experiment using advanced spectroscopic techniques was established to resolve the internal evolution of compressed axial (Bz) and azimuthal (Bθ) magnetic fields.

1.2 Z-Pinch Principle and Practical Considerations: In a Z-pinch, axial current driven through a cylindrical plasma interacts with its self-generated azimuthal magnetic field via the Lorentz force (j x B), causing radial implosion. The process encompasses breakdown/ionization, implosion, and stagnation.

• Single-fluid MHD equations describe mass continuity, momentum balance, Ohm’s law, and thermal energy balances for ions and electrons.
• Ideal MHD simplifies these under infinite conductivity assumptions to yield equilibrium Bennett relations and 1D self-similar scaling.
• The Snow-Plow Model provides 0D estimates of shell implosion, accounting for swept mass, magnetic pressure forces, and circuit inductance coupling (L_total = L_PPS + L_plasma).

1.3 Spectroscopic Diagnostics of Plasma: Emission spectroscopy provides non-invasive diagnostics:

• Doppler broadening yields ion temperatures (Ti) and velocity distributions.
• Stark broadening and shifts determine electron density (ne) for non-hydrogenlike isolated lines (e.g., Ar III at 3302 Å, 2884 Å, and Ar IV at 2913 Å).
• Line intensity ratios between spectral lines determine electron temperature (Te) through collisional-radiative (CR) and LTE modeling.
• Zeeman splitting provides magnetic field strength; in dense plasmas where Stark broadening dominates, polarization-resolved techniques (comparing π and σ lineshape widths or σ+ and σ- shifts) permit sub-Tesla to multi-Tesla field measurement.

Chapter 2: Experimental Setup

The setup uses a pulsed-power generator discharging four 4-μF capacitors (16 μF total at up to 23–30 kV, producing ~300 kA with a 1.6 μs rise time). A quasi-static axial magnetic field up to 0.4 T is generated using Helmholtz coils (rise time ~5 ms). An annular gas puff nozzle produces a hollow cylindrical shell of argon gas (diameter ~38 mm outer, ~14 mm inner) across a 10 mm A-K gap.

Spectroscopic diagnostics utilize:

1. A 1-m spectrometer coupled to a gated ICCD camera and bifurcated fiber bundles for σ+/σ- circular polarization measurements of Bθ.
2. A 0.5-m imaging spectrometer coupled to a polarizing beam-splitter to record π and σ linear polarization components of laser-ablated Al dopant emission for Bz measurements.
3. Visible framing cameras and Mach-Zehnder/Michelson laser interferometers (532 nm) to measure gas density profiles and plasma implosion dynamics.

Chapter 3: Results

3.1 Simultaneous Measurements of Azimuthal and Axial Magnetic Fields: Simultaneous measurements of Bz and Bθ at z = 3.5 mm revealed that Bθ in the imploding shell remains nearly constant (~1.5–2 T) and substantially smaller (by a factor of ~4) than predicted by total circuit current, indicating ~75% of current flows in the peripheral low-density plasma at larger radii. Bz at stagnation reaches ~2.9 T (a ~15x compression of initial 0.4 T field), exceeding Bθ due to plasma inertia (‘overshoot’). The Bz flux confinement efficiency is estimated at ~50%.

3.2 Axial Magnetic Field Distribution Along z-axis: Bz shows an axial gradient during late implosion/stagnation: the field near the metal anode (z ~ 1 mm) is approximately half of that at mid-gap (z ~ 5 mm) because magnetic flux remains anchored/frozen in the solid electrode.

3.3 Effects of Axial Magnetic Field on Plasma Implosion:

• Magneto-Rayleigh-Taylor Instabilities (MRTI): Pre-embedded Bz significantly stabilizes the implosion, reducing MRTI growth rates, decreasing perturbation amplitudes (by ~20% at 0.1 T and ~50% at 0.2 T), and increasing perturbation wavelengths.
• Filament-like Structures: For Bz0 = 0.2 T, helical-like filaments develop along the combined (Bz + Bθ) field direction. Lineout analysis reveals that filaments have 10–20% higher electron density and slightly lower electron temperature compared to the ambient plasma.

Chapter 4: Discussion

The unexpected current loss to the peripheral plasma is modeled using a force-free current configuration in the low-density peripheral region (LDP). Analytical derivations of electron and plasma equations of motion demonstrate that in the presence of an axial field Bz, the transformed electric field in the plasma rest frame E_pl is non-zero (unlike Bz = 0 where E_lab ⊥ Bθ leads to E_pl = 0). This drives axial and azimuthal current components (jz and jθ) in the low-density plasma on a fast timescale (τ_steady ~ 15 ns), keeping the peripheral plasma force-free without rapid inward implosion.

Chapter 5: Conclusions & Appendix

Conclusions:

1. Successful simultaneous, non-invasive measurement of compressed Bz and driving Bθ during Z-pinch implosions.
2. Demonstration that pre-embedded Bz induces a major redistribution of axial current into the low-density periphery via force-free current mechanisms.
3. Quantification of Bz confinement efficiency (~50%) and discovery of axial Bz gradients caused by electrode flux pinning.
4. Verification that pre-embedded Bz effectively mitigates MRTI.

Appendix:

• A.1 Analytical derivation and dispersion relation for the development of force-free current configurations in low-beta magnetized plasma.
• A.2 Guiding-center velocity solutions for collisionless electron motion in crossed E and B fields.
• A.3 Steady-state velocity and current transport derivations for collisional electrons in combined electric and magnetic fields.