PHYSICS OF PLASMAS 15, 042307 ͑2008͒ Nonlinear electron magnetohydrodynamics physics. I. Whistler spheromaks, mirrors, and field reversed configurations ͒ R. L. Stenzel,a J. M. Urrutia, and K. D. Strohmaier Department of Physics and Astronomy, University of California, Los Angeles, California 90095-1547, USA ͑Received 7 December 2007; accepted 3 March 2008; published online 22 April 2008͒ The nonlinear interactions of time-varying magnetic fields with plasmas is investigated in the regime of electron magnetohydrodynamics. Simple magnetic field geometries are excited in a large laboratory plasma with a loop antenna driven with large oscillatory currents. When the axial loop field opposes the ambient field, the net field can be reversed to create a field-reversed configuration ͑FRC͒. In the opposite polarity, a strong field enhancement is produced. The time-varying antenna field excites whistler modes with wave magnetic fields exceeding the ambient magnetic field. The resulting magnetic field topologies have been measured. As the magnetic topology is changed from FRC to strong enhancement, two propagating field configurations resembling spheromaks are excited, one with positive and the other with negative helicity. Such “whistler spheromaks” propagate with their null points along the weaker ambient magnetic field, with the current density localized around its O-line. In contrast, “whistler mirrors” which have topologies similar to linear Ͼ whistlers, except with Bwave B0, have no null regions and, therefore, broad current layers. This paper describes the basic field topologies of whistler spheromaks and mirrors, while companion papers discuss the associated nonlinear phenomena as well as the interaction between them. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2903065͔ I. INTRODUCTION magnetohydrodynamic ͑MHD͒ configurations such as spheromaks18–20 or mirrors. Whistler waves are possibly the oldest plasma waves Investigating the properties of nonlinear wave packets 1,2 known. Although their linear properties are well forms the basis for understanding strong whistler turbulence, 3,4 documented, the regime of large amplitude whistler is still which occurs in magnetic reconnection geometries,21,22 mag- a topic of current research in space and laboratory plasmas. netospheric and solar plasmas,23,24 cometary tails,25 and plas- Nonlinear phenomena occur when the wave perturbs those mas with weak background magnetic fields such as in the plasma parameters which affect its propagation, typically ionosphere of Venus.26,27 density and magnetic field for whistlers in cold plasmas. The work is presented in a series of several companion When collisions and kinetic phenomena are included, a papers. Part I describes the field topologies, Part II28 the change of the electron distribution by strong whistlers will nonlinear propagation and wave-wave collision phenomena, also create nonlinear phenomena.5 Density perturbations cre- Part III29 the electron energization, Part IV30 the secondary ate modulational instabilities like filamentation,6–9 envelope whistler instabilities created by modifying the electron dis- 31 solitons,10,11 and parametric instabilities.12,13 Less is known tribution, and Part V discusses triggered whistler emis- about nonlinear effects of whistlers with “large” wave mag- sions. The experimental setup and measurement techniques are mostly explained in Part I and referred to in the other netic fields, defined here as wave fields, Bwave, exceeding the papers. ambient static magnetic field, B0. Since the whistler disper- sion depends on the magnetic field, a large wave can be expected to propagate at a different speed and direction from a linear wave. It is not obvious how the wave would propa- A. Experimental setup gate if it creates a magnetic null point. Theoretical solutions for two- and three-dimensional vortices have been The experiments are performed in a large ͑1 m diam, published,14–17 but do not address wave propagation. The 2.5 m length͒ pulsed dc discharge plasma generated with a present work answers such questions from an experimental 1 m diam oxide-coated cathode shown schematically in ͑ Ӎ 12 −3 Ӎ viewpoint. It is demonstrated that whistler modes with Fig. 1. The parameter regime ne 10 cm , kTe 2 eV, տ ͒ Bwave B0 do exist, how they propagate and interact with B0 =5–10 G, 0.4 mTorr argon is that described by electron other waves, and how they energize the electrons and, finally, MHD ͑EMHD, magnetized electrons, unmagnetized ions32͒. that the modification of the electron distribution function Insulated magnetic loop antennas ͑2–4 turns, leads to whistler instabilities. The field topologies of 10–30 cm diam͒ are inserted into the plasma center and a wave packets are measured and compared with well-known charged ͑1200 V͒ capacitor ͑0.1–10 ␮F͒ is discharged into the loop using a fast, high current transistor. This results in a a͒ Ӎ URL: http://www.physics.ucla.edu/plasma-exp/. Electronic mail: weakly damped oscillatory current Imax 100–300 A, which / [email protected]. decays with period T=2␲͑LC͒1 2 Ӎ5–50 ␮s, an example of 1070-664X/2008/15͑4͒/042307/8/$23.0015, 042307-1 © 2008 American Institute of Physics Author complimentary copy. Redistribution subject to AIP license or copyright, see http://php.aip.org/php/copyright.jsp 042307-2 Stenzel, Urrutia, and Strohmaier Phys. Plasmas 15, 042307 ͑2008͒ 1 m cathode 160 A Langmuir Coil and anode Iloop and coax probe y Vloop 0 B z B0 1.5 m x 1kV 0.15 MW ≈ 12 −3 ne 10 cm ≈ Ploop 3D Magnetic kTe 3.0 eV probe B0 =5G 0 pn = 0.4 mTorr (Ar) 2.5 m 0.135 J Plasma FIG. 1. Schematic of the experimental setup and relevant parameters. Uloop Vacuum which is shown in Fig. 2. In vacuum, the magnetic field in the center of the loop at the peak current can be as large as B B 0 =100 G 0 =5–10 G. 0 5 10 15 20 Figure 2 shows the measured antenna voltage and cur- t(µs) rent waveforms as well as the calculated instantaneous power and the energy deposited into the antenna. The dissipation in FIG. 2. Measured antenna current and voltage vs time at the antenna input vacuum occurs mainly in the resistance of the antenna and terminal. Calculated instantaneous power P͑t͒=I͑t͒V͑t͒ and energy ͐ transmission line since the free space radiation resistance is U= Pdt. In vacuum the energy loss by the circuit resistance is small com- pared to that by the radiation resistance in plasma. negligibly small. However, in the high-beta plasma, a large amount of energy is transferred into whistler modes which is evident from the increase in damping, measured by the time currents, B , from those created by antenna currents, ␶ / plasma constant =2L R. There is also a small increase in the ring- Bcoil, and to demonstrate important differences in the axial ͓␻ ͑ −1 −1 ␶−2͒1/2͔ ing frequency, = L C − , which is dominated by field direction relative to B0. a decrease in inductance L rather than the increase in damp- A Langmuir probe is also attached next to the magnetic ing. The radiation resistance due to whistlers is found to be probe so as to measure the plasma parameters in three- ͑␶−1 ␶−1 ͒Ӎ ⍀ ⍀ ⍀ Rrad=2L plasma− vacuum 7.1 −2.3 =4.8 . For a peak dimensional ͑3D͒ space and time. Typically, at a given probe 2 / current of 150 A, the wave power ImaxRrad 2=54 kW position, the probe voltage is fixed and the current is re- represents a significant fraction of the applied power corded versus time, then the voltage is incremented in small / ͑ ͒͑ ͒/ Ӎ Pin=ImaxVmax 2= 1200 V 150 A 2 90 kW. steps so as to obtain the time-resolved current-voltage traces. Further useful information is obtained in Fig. 2 from the time-resolved energy deposition. After the first half cycle of II. EXPERIMENTAL RESULTS the current waveform, only Ϸ5% of the peak energy is lost A. Single antenna current pulse in vacuum, while in plasma about Ϸ50% is deposited. In the second half cycle, when whistler spheromaks are excited, the We review briefly the excitation of EMHD fields by a fraction of energy deposition is even larger. These values single current pulse which have been reported in detail will later be compared with the internally measured magnetic earlier.33–36 Here, a current pulse in the form of a single field energy. half-sine wave is applied whose polarity is chosen so as to The local magnetic field is measured with a single mag- produce an antenna field opposing the ambient field. The netic probe containing three orthogonal small loops antenna field is larger than the ambient field, hence the net ͑5 mm diam͒ which can be moved along three coordinates, r, field on axis near the coil becomes reversed. ␪,z. The space-time dependence of the field B͑r,t͒ is ob- Figure 3 shows contour maps of the net axial magnetic ͑ ͒ ͑ ͒ tained from rapidly 1Hz repeated experiments which are field component Bz x=0,y,z at different times during the highly reproducible ͑␦n/nϽ3%͒. The probe signals are re- antenna current pulse. The time is indicated by the end of the corded with a four-channel digital oscilloscope with up to antenna current waveform inserted into the lower left corner 1 ns time resolution, averaged over 10 shots at each position of each frame. The total magnetic field consists of the axial ͑ ͒ to increase the amplitude resolution 10 bits . The data pro- dc magnetic field, B0, the field produced by the coil current, ͑ ϰ / ͒ cessing includes integration Vprobe −dB dt , coordinate and the field due to induced plasma currents. In the presence transformation from ͑r,␪,z͒ to ͑x,y,z͒, spatial differentiation of plasma, the penetration and decay of the time-varying ͒ ͑ ϫ /␮ٌ to obtain the current density, J= B 0, and integration to field-reversed configuration FRC is delayed.