SCHOOL OF PHYSICAL SCIENCES

LOW POWER, LONG DURATION ROTAMAK DISCHARGES IN ARGON

B.L. JESSUP and J. TENDYS

FUPH-R-180 FEBRUARY, 1982 LOW POKER, LONG DURATION ROTAMAK DISCHARGES IN ARGON

B.L. Jessup and J. Tendys*

School of Physical Sciences The Flinders University of South Australia Bedford Park, 5042, Australia

ABSTRACT

An investigation was made of a Rotamak compact torus configuration in which the rotating magnetic field used to drive the toroidal current was generated by a pulsed 6 KW R.F. oscillator. The toroidal current was measured together with the vertical component of the magnetic field both along the vertical axis and as a function of radius in the midplane of the current ring. The experimental results show that a Rotamak equilibrium, apparently stable for several milliseconds, could be obtained. Toroidal plasma currents of several hundred amps were observed with argon filling pressures around 0.2 mTon and applied vertical equilibrium fields of about 1 m Tesla.

* Visiting Scholar, on attachment from the Australian Atomic Energy Commission. 1.

I. INTRODUCTION

The R^tamak concept, which uses a rotating magnetic field to drive the steady toroidal current in a compact torus device, has been studied experimentally using high power (10 Mm"), short time (60 usee) rotating magnetic field pulses produced by line generators (W.H. HUGRASS, I.R. JONES,

K.F. McKENNA, N.G.R. PHILLIPS, R.G. STORER, and H. TUCZEK, 1980). It is of considerable interest to extend this study to longer lived Rotamak plasmas-

The objective of these experiments was to verity the maintenance of an equilibrium configuration of milli-second lifetime.

In this report we describe the construction of a Rotamak device which uses a low power (6 KW) C.W. oscillator. Due to heating of the circuit components used to couple the RF powe- to the rotating field coils, the rotating magnetic field pulse was rarely allowed to exceed 12 ms. The

Rotaaak equilibrium field configuration was studied during this time interval using magnetic probes and a current loop, which was used to monitor the total toroidal current.

II. EXPERIMENTAL APPARATUS

2.1 Vacuum System

The spherical vacuum vessel was made of pyrex glass with a 0.135 m radius, and had two diametrically opposed 0.05 • diameter ports, Fig. 1.

One port was used for the pressure gauges, while the other was used for pumping and gas input. When experiments were not in progress the vacuum vessel was maintained at a base pressure of 3 x 10' Torr by means of a

6" alcatel oil diffusion pump fitted with a Balzer water-cooled baffle and backed by a two stage rotary pump. During the experiments argon gas was allowed to enter via a 4 an I.D. pyrex tube attached to one of the ports. •>

The gas was permitted to flow continuously into the system maintaining an equilibrium pressure, controlled by a needle valve. The gas pressure in the vessel was monitored between plasma discharges by a Cooke ionization gauge.

2.2 Rotating Magnetic Field Generator

The rotating magnetic field power source was a 6 KW Class C oscillator which was tuned to 0.845 MHz. The oscillator tank inductance consisted of two sections connected in series. One section was modified to permit the powsr to be taken out by inductive coupling. This modified part of the tank circuit inductance was made from 0.01m O.D. copper tube formed into three sections of three turns each with a diameter of 0.13 m, Fig. 2.

The two secondary coils each 0.08 m in length, made from 11 turns of

0.005 m O.D. copper tube, had a diameter of 0.13 m. and an inductance of

30 WH each. Each secondary coil was supported on a hinge in one of the two gaps in the modified tank inductor to permit the coupling with the primary to be varied.

A variable capacitor was connected in series with each secondary coil and adjusted so that the series resonance frequency of the secondary circuit matched that of the tank circuit. The coupling of the secondaries was then adjusted until maximum power was fed into each of the two 50(2 output cables. During the adjustment both cables were terminated by 50ft resistive loads.

One of the two output cables had an additional 60 m length of cable added to it which delayed the current in that arm by 0.3 us to give a 90° phase shift between the currents in the two outputs. It should be noted that the use of a delay line to obtain the required current phase shift for the generator of the rotating magnetic field presented a problem.

When the length of a cable is exactly an odd number of quarter wave lengths, 3.

as was the case with the delay cable used in these experiments, then the input impedance Z of the cable is given by

Z 2

where ZQ is the cable iapedance and Z, is the load impedance (F.E.

TERMAN, 1943). Accordingly if Z,, which is nominally 50ft, gains a small capacitive or inductive component then Z will no longer be SOQ but will have a large reactive component.

The load coils were connected to the 50ft cables by matching circuits,

Fig. 2. The matching conditions are given by

2 Cj = l/(w LL - uwi0RL - R^')

Ll s Cl RL2/(tt)2LL Cl " 1} * (u2LL Cl " 1W

changes in the reactive part of the load at the tank coil; consequently the oscillator experienced large changes in its load. This caused shifts of about 1% in the operating frequency. This interaction was reduced by

connecting a 100(2 resistor to ground at the input to the delay cable.

Thus the adjustment of L. and C. was made easier at the expense of some of the output power from the oscillator.

2.3 Rotating Field Coils

The rotating field coils fixed to the vessel consisted of two

orthogonal Helmholtz coils. Each Helaholtz coil was made from 0.005 m O.D.

copper tube formed into two coils of 3 turns of diaaeter of 0.27 m. The

vacuum inductance of each Helaholtz coil was 12 yH.

Although the two Helaholtz coils were nominally orthogonal there was 4.

a mutual inductance of about 80 nH between thea. This had to be eliminated so that the two impedance aatching circuits could be adjusted independently. This was achieved by coupling the two circuits with a small variable mutual inductor formed by two loops with an adjustable separation. By choosing the sign of this mutual inductance to be opposite to that already present the net coupling could be made very small.

The presence of pla'jaa changes the impedance of the rotating field coils; in practice the values of L, and Cj in the impedance aatching circuit were adjusted with a plasaa present in the vessel. A Pearson current transformer was used to measure the input current to the matching circuit and a potential divider the voltage input. The values of L. and C. were then varied until the input resistance was close to the 50Q of the cables.

2.4 Equilibrium Vertical field

An externally imposed vertical field is required to maintain equilibrium. In this experiment each of the two vertical field coils were constructed from 133 turns of 1 am O.D. copper wire wound on circular formers. Each coil had a mean diameter of 0.35 m and an inductance of

10 mH. The coils were positioned equal distances above and below the discharge vessel with a coaxial separation of 0.5 a. Current was fed to the coils from a capacitor bank consisting of four 300 uf capacitors connected in parallel. The bank, fired by triggering an SCR, gave an asyaaetrical current pulse with a first half period of 18 as. At the peak of the pulse the current reaained constant for 2 as to better than 10%.

The systea was designed to supply a vertical field strength of 10 aTesla at the centre of the discharge vessel. However, it was found experiaentally that fields of only about 1 mTesla were needed. The vertical field was applied in the negative z-direction. s.

2.5 Pre-ionization

At pressures of less than 1 aTorr of argon the rotating magnetic field was insufficient to break down the gas electrically. To overcoae this problem the gas was very weakly preionized by creating an R.F. discharge in the vessel. The mechanism by which the R.F. discharge was created was not well understood and the final experiaental configuration of exciting coils discussed below was obtained by a process of trial and error.

A signal generator was used to drive a 300 watt broad-band power amplifier. The output of the amplifier was connected to two coil structures made of 2 am O.D. copper wire, Fig. 1. The first of the two structures was a four turn coil of diameter 0.15 a. The second consisted of two short solenoids, 6 and 4 turps respectively, wound on the neck of the vessel and separated by 0.06 a. All the coils were electrically connected in series. In addition the aluainiua end plates fitted to the discharge vessel (see Fig. 1) were electrically connected to the output cable of the amplifier so that a tiae varying potential was generated along the length of the vessel.

This configuration, although quite arbitary, proved successful in preionizing argon at pressures down to 0.1 aTorr. The lower pressure

liait corresponded to the mean free path length of the electron becoming

comparable to the dimension of the vessel. The optimum oscillator

frequency was found to be somewhat pressure dependent. Frequencies in

the range 13-26 PWz were used.

III. DIAGNOSTICS

3.1 Introduction

A preliminary investigation of the Rotamak plasma was made by

measuring, 6.

(i) the total toroidal current

(ii) The :-component of the total magnetic field both as a function of

radius along a line in the 2=0 plane, b (r,o), and as a function

of z along the z-axis, b (o,z), Fig. 1.

These measurements were difficult because the induced voltages were very small. This was because the Rotamak magnetic field configuration changed with a characteristic time of several milliseconds. Therefore, both the current loop and magnetic probes had to have a high sensitivity.

This was achieved by using many turns, amplification and integrating with an active integrator. The relevant circuit is drawn in Appendix 1.

Additionally low pass filters were used to remove the high frequency pick up associated with the preionization RF and the rotating field. The three stage filters were constructed using feed-through capacitors to

•iniaize the stray inductance and each RC pair was placed in a separate shielded compartment. The response curve is given in Fig. 18.

All calibration factors in the following text refer to the complete system of probe or current loop together with its electronics.

3.2 Current Loop

The current loop consisted of 4265 turns of 39 SWG wire on a 0.43 m length of plastic tube of 4 mm O.D. The current loop resistance was measured to be 70(1 and its inductance, calculated using Nagaoka's formula, was 670 wH (F.tf. GROVER, 1946), The signal from the current loop was carried to the Faraday cage using 50(2 triaxial cable. Inside the Faraday cage, the signal was terminated with 50(2 and the voltage signal filtered, amplified and integrated. The calibration factor was determined to be

6.9 A/mV. 7.

3.3 Magnetic Probes

Two magnetic probes were used to measure the total Magnetic field component. The first, consisting of 258 turns of 39 SNG, was wound on a hollow plastic cylinder 10 ma in length. This design enabled it to move coaxially along the current loop coil so that the two could be used

simultaneously. Fig. 1. It had a resistance of 340 and a calibration

factor of 0.58 gauss/mV. This probe was used to measure b (o,z).

The second probe coil had 169 turns of 39 SNG and was rectangular

in shape, 13 ma by l.S ma. The probe calibration factor was 0.66 gauss/aV.

It was used to measure b (r,o).

3.4 Monitoring of RF Currents in Helmholtz Coils

In addition to the above diagnostics it was necessary to monitor

the rotating magnetic field currents in the Helmholtz coils. Small current

transformers were placed on the input lead of each of the Helmholtz coils.

The current traces from these coils were directly displayed on an oscillo­

scope to monitor the rotating field current pulse duration. It was also

important to monitor the phase difference between the two currents as a

function of time. This was achieved by the circuit in Appendix 2 which

gave an output proportional to the phase difference between the currents.

The circuit converts the incoming signals into a pulse train of constant

amplitude whose mark-space ratio is proportional to the phase difference.

The pulse train is then averaged by an integrator with a SO vis time

constant to give the output voltage.

IV. EXPERIMENTAL RESULTS

4.1 Vacuum Rotating Field

An examination of the radial distribution of the vacuum rotating

magnetic field produced by two orthogonal Helmholtz coils was made before 3.

commencing the plasma experiments. This was done to permit a comparison with the radial distribution of the rotating magnetic field with a plasma present to give an indication of the degree of penetration of the field.

It was assumed that the radial distribution of the vacuum rotating magnetic field was independent of the matching circuit settings, provided that the currents in the two coils were equal and 90 out of phase.

To permit the observation of the rotating magnetic field at the centre of the vesse* the current loop was removed. This allowed a calibrated magnetic field probe to be inserted vertically into the vessel so that the probe coil axis could be positioned parallel with the axis of either of the Helmholtz coils. Initially the probe was tested by rotating it through an angle of 180° with one of the two Helmholtz coils electrically disconnected. The resulting magnetic field was found to be maximu* when the axis of the probe was parallel to the axis of the

Helmholtz coil which was electrically connected and very close to zero at a rotation of 90 to this. Nhen the two Helholtz coils were electrically connected, the resultant magnetic field was found to be approximately constant while the probe was being rotated through 180 .

A typical plot of the radial variation of the vacuum rotating magnetic field on the mid-plane of the vessel is shown in Fig. 3.

4.2 Penetration of the Rotating Magnetic Field

After the above measurement was completed the impedance matching circuit was tuned with an argon plasma present in the vessel. The magnetic probe used in the previous section was positioned and orientated in such a manner that a radial scan of the 6 component of the rotating magnetic field, bo, in the Z« 0 plane could be made. The results of

two such scans are shown in Figs. 4 and 5. The figures show bQ plotted

as a function of radius for various times during the discharge for initial 9.

argon gas filling pressures of 0.11 and 0.14 nTorr respectively. These diagrams indicate that the rotating aagnetic field has penetrated the argon plasma.

4.3 Observation of the RF Currents in the Helmholtr Coils

The output signals of the two current probes which were used to monitor the IF current in the Helnholtz coils were recorded at all times.

It was found that although the phase difference during the plasma discharge night vary from 90° by as much as 30° during the discharge, shot-to-shot reproducibility for a given initial gas filling pressure and applied vertical field was excellent.

The variation AB in the amplitude of the rotating magnetic field B during the plasma discharge can be written as a function of the deviation

A8 of the phase angle from 90° as

££~ 1 - (1 - sin M)* 0

To first order this can be written as

AB _ A6 T T where A6 is in radians. Hence, as an example for A6 = 30°, AB/B ~ 0.2S. Typically the phase variation was less than half this.

4.4 Magnetic Probe Results

As a guide to finding sets of interesting working parameters for the

Rotamak experiment the total toroidal current, I., and b_(o,o) were measured for different combinations of initial gas filling pressure and applied vertical field. Two clear trends were found. Firstly, Fig. 6A shows that the maximum values of I. increases with the applied vertical field. However, !0

there was a limit to the amplitude of the vertical field which could be used. If this applied field was too strong electrical breakdown of the »vs was not possible. It is conjectured that a better preionization

technique would overcoat this problem. Secondly, bz(o,o) was found to increase with decreasing gas filling pressure (see Fig. 6t). The lowest pressure at which it was still possible to preiouize the gas was 0.1 •Torr.

Three plasaa parameter configurations were studied in detail.

For the first, a 3 as rotating field pulse was applied during the tine for which the applied vertical field remained reasonably constant.

For the other two, the rotating magnetic field was switched on 190 us after the triggering of the applied vertical field bank. Therefore the applied vertical field was increasing in nagnitude during the rotating field pulse. This procedure allowed the g..s to be ionized while the magnitude of the applied vertical field was small. Once the gas was ionized, it was possible to maintain the discharge for applied vertical fields considerably greater than those for which the gas could be broken dOWfc.

Case 1

Figure 7A shows a typical oscillogram of i.(t) and b (o,o) for a fillin;' pressure of 0.14 mTorr and a peak applied vertical field of

0.75 nTesla. The upper trace shows the total toroidal current driven by the rotating magnetic field. The lower trace shows that the amplitude of this current is sufficiently large to reverse the direction of the applied vertical field during the tine for which the current flows.

Figure S displays the variation of bz(r,o). The poloidal flux defined by

*(r,o) - 2» J r» bx(r\o) dr' o

is presented in Fig, 9. The variation of bz(o,z) along the vertical axis 11.

is shown in Fig. 10. One notes that at the three representative times

chosen the separatrix is positioned well inside the wall of the discharge

vessel. The ratio a of the distances from the centre of the vessel to

the separatrix and to the null point on the vertical axis reached a

maximum value of 1.1 after about 1 ms of applied rotating magnetic field.

The magnetic configuration, consequently, was oblate at all times.

Case 2

The initial conditions corresponding to the oscillogram shown in

Fig. 7B are an argon filling pressure of 0.21 mTorr and an applied

vertical field which reached a maximum of 1.1 mTesla after 6 ms. For

this particular case the duration of the rotating magnetic field pulse was increased to 12 ms. The plots of b,(r,o), *(r,o) and b (o,z)

corresponding to these initial conditions are shown in Figs. 11, 12 and

13 for four representative times. From these graphs it is seen that

the position of the magnetic axis, separatrix and null point remains

constant after 4.8 as. Again, the configuration remains well confined

and apparently stable as long as the rotating field is applied.

Case 3

For the third case considered the initial argon gas filling pressure

was 0.11 mTorr and the peak value of the applied vertical field was

0.94 mTesla. The corresponding traces of I^(t) and bz(o,o) are shown

in Fig. 7C. From the I At) signal it is seen that the toroidal current

cuts off rapidly after 3.5 ms even though the rotating magnetic field

pulse, not displayed, continued to be applied. The cause of this cutoff

in the current is not known. Inspection of Figs. 14, IS and 16 which

display b (r,o), I.(r,o) and b (o,z) gives a clear picture of how the

magnetic configuration changes prior to the loss of the plasma. The

experimental plots show that as the magnitude of the applied vertical 12. field increases the magnetic axis, separatrix and null point all move progressively closer to the centre of the vessel. After 2 ms I. reached a peak value of 250 amps and decreased. However, the average current density (obtained by dividing 1 by the area enclosed by the separatrix) is increasing at all times.

4.5 Power Measurements

An experimental estimate of the power delivered to the Rotamak plasma from the oscillator was made. Using a Pearson current transformer and a voltage probe, the input current and voltage to each arm of the impedance matching circuit was measured with and without plasma in the vessel. Simultaneously the current in each of the Helmholtz coils was measured. If one makes the assumption that the losses in the impedance matching circuit are negligible, which seems reasonable as it is known the components involved are of high Q, then the equivalent load resistance is given by

V I _ IN MN

L 2 ~ I coi•l,

V-N and I.N are the input voltage and current respectively and I .. is the current flowing in the Helmholtz coil. R, was measured to be 1.2(2 without plasma and 5.5ft with plasma. These values were obtained by averaging over several shots. The power dissipated in the plasma is given by

P " 2 l2coil {RL_ ' RL } (3)

c011 plasma Sracuum

The average measured current in the rotating field coils was 25 amps RMS;

using equation (3) P was 5.4 Kw. An estimate of the errors in the above measurements gave the result that the actual power absorbed by the plasma was between 2.5 Kw and 6 Kw. 13.

V. DISCUSSION AND CONCLUSION

Axisymmetric toroidal equilibria are described oy solutions of the Grad-Shafranov equation

r 37 IF 5?J + ^T = " yor 3*= " % r C-

(This particular form of the Grad-Shafranov equation refers to the situation where B . . ^ = 0.) In the above equation ip is defined as

<|>(r,z) = (r'b: (r\z) dr' . o

Further, it can be shown that all field quantities can be expressed as functions of • •

While the experimental results presented in this report are preliminary they are informative when they are analysed using the Solovev solution of the Grad-Shafranov equation, namely

2 °2 *2 . i (4) * - * V...) ir [j£ R2

where R is the position of the separatrix, bz(o,o) is the total vertical

field on axis at z * 0, and a is the ratio of the radius of the separatrix

to the height of the null point. This solution is obtained on assuming

that pa* (L.S. SOLOV'EV and V.D. SHAFRANOV, 197). If furthermore we

assume that the electrons are tied to the rotating magnetic field lines

the Solovev solution implies that the electron number density is uniform

and given by

4 bz(o.o) o2 y„ e ui Rz * o

where y is the permeability of free space, e is the electron charge and

u the angular frequency of the rotating magnetic field. In addition

one can write 14.

1 = Nef where N is the total number of charge carriers and f = W/2TT. The

Solovev solution predicts that the ratio £ of the radius of the separatrix and that of the magnetic axis is a constant, equal to /Z. Finally the solution predicts that the temperature of the electrons and ions (assumed equal) at the magnetic axis is given by b (o,o) e u R2 T = —

16 k where k is Boltzaan's constant.

To see if the experimentally measured configuration is reasonably modelled by the Solovev solution, the quantity \\i/ii from equation (4), was compared with the normalized, measured values of $. The fit of the theoretical curve to the experimental data was in general quite good. A representative example of such a fit is shown in Fig. 17, corresponding to the data in Fig. 9 taken at 6 ms. Further, the experimental data displayed in Figs. 11, 12 and 13 corresponding to oscillogram Fig. 7B indicate that the configuration reaches an equilibrium such that the ratio £ remains fairly constant at a value of 1.4 for times 4.8 to

7.2 ms. This is close to /2.

In view of the apparent agreement between the Solovev solution and the experimental data we used the solution to calculate the temperature at the magnetic axis and the electron number density, b (o,o) and R can be read from Figs. 11 - 13 and have the values of 0.79 mTesla and 0.11 m respectively. The frequency, f, was 0.84S Mlz. Substitution of this data into equation (6) yields a temperature of 3 eV. The Solovev model uniform number density is given by equation (5). From Figs. 12 and 13 17 3 a is calculated to be 1.22 which yields n = 3,4 x 10 particles/m . The initial argon filling pressure was 0.21 mTorr which corresponds to 18 3 7.4 x 10 particles/m . Therefore the Solovev model predicts the plasma to be about S% ionized. 15.

Finally we can use the rigid rotor model to predict a value for

I.. The plasma volume can be written as

v - iw R3

3 a and therefore

N = nV = l.SS x 1015 .

Thus

I. = Nef = 209 amps .

The experimentally observed average value of I., between 4.8 to 7.2 ms, was 350 amps. Although the experimental toroidal current is somewhat higher than the calculated value, the agreement is good considering the

simplicity of the model.

In conclusion our experience suggests the following improvements could be made to the experimental apparatus.

(1) The impedance matching circuit proved to be a clumsy way to match

the 50ft cables to the Helmholtz coils. This circuit should ideally

be replaced by one using step down power transformers which, together

with a series capacitor, should be easier to tune provided the Q

is not too high.

(2) The vertical magnetic field coils could be D.C. pulsed to allow

longer duration experiments.

(3) A more efficient preionization technique needs to be applied. This

improvement would allow one to use lower initial gas filling

pressures and thus obtain a more highly ionized plasma.

Future development of the experiment will hopefully lead to the

replacement of the 6 KM oscillator by two separate high power R.F,

amplifiers fed by indepndent signal sources with output current dephased

by 90°, and the study of deuterium plasmas. 16.

ACKNOWLEDGEMENTS

The authors would like to thank Professor I.R. Jones and Dr. W.

Hugrass for their support and discussions during this work and Dr. N.

Clark for providing the generator. / Financial support, for which we are grateful, was provided under the National Energy Research, Development and Demonstration Program administered by the Commonwealth of Australia Department of National

Development and Energy, by the Australian Institute of Nuclear Science and Engineering and by the Australian Research Grants Committee.

REFERENCES

W.N. Hugrass, I.R. Jones, K.F. McKenna, M.G.R. Phillips, R.G. Storer

and H. Tuczek, Phys. Rev. Lett., 44 (1980) 1676.

F.E. Terman, "Radio Engineers* Handbook" McGraw-Hill, 1943.

F.W. Grover, "Inductance Calculations. Working Formulas and

Tables", Dover, 1946.

L.S. Solov'ev and V.D. Shafranov, Reviews of Plasma Physics, 5,

1-248 (1970). APPENDIX 1

The circuit used to aaplify and integrate the probe and current loop signals APPENDIX

Circuit for phase comparator for RF currents FIGURE CAPTIONS

Schematic diagram of the experimental apparatus.

Schematic diagram of the rotating magnetic field circuit.

Radial variation of the vacuum rotating magnetic field

in the midplane of the vessel.

Radial variation of the rotating magnetic field in

midplane of the vessel with plasma for Argon at 0.11 mTorr.

Radial variation of the rotating magnetic field in the

midplane of the vessel with plasma for Argon at 0.14 mTorr.

Variation of I. with applied vertical field.

Variation of b (0,0) with initial gas filling pressure.

Oscillogram showing I and b (0,0) traces: Argon 0.14 raTorr.

Oscillogram showing I, and b (0,0) traces: Argon 0.21 mTorr.

Oscillogram showing I. and b (0,0) traces: Argon 0.11 mTorr. b (r,o); Argon 0-14 mTorr.

$(r,o); Argon 0.21 mTorr b,(o,z); Argon 0.21 mTorr. b_(r,o); Argon 0.11 mTorr.

$(r,o); Argon 0.11 mTorr b,(o,z); Argon 0.11 mTorr.

Fit of Solovev model to experimental data.

Filter response curve. ix w: 3 3, 3, O O O •» I 1 oH >i •* 1 •I 1

Current Loop

Ionization Gauge

Radial Probe Port

Helaholtz Coil Pairs

Puinping Port

Preionization

FIGURE 1 Oscillator Tank Coil

SOR RG8 Cable L ~ 1 liH C. ~ 3 nf

•O ©

C^mdo^SZ^ o vw

60 » Delay Cable / Impedance Matching Load Helmholtz Coil 12 uH Additional Added Resistance Circuit (without plasma)

FIGURE 2 2.0

1.8

1.6

1.4

1.2

| 1.0

CD

0.8

0.6

0.4

Nail 0.2

J I 61 !8 1k0 412 L14 Radius (ca)

FIGURE 3 2 i- 0.5 Rotating Magnetic Field Strength in Arbitrary Unit* o o VI VI VI v» b T

1*

7liu s « 1 «/» 8

4* e In 8 L 8 I L 400

300 -

< 200

c u 100 a u

-L -L ± 0.5 1.0 1.5 Applied vertical field (mTesla)

FIGURE 6A

l.Oi—

0.8

in 0.6 5 o * o•H 0.4

0.2

± J- ± 0.1 0.2 0.3 0.4 Filling pressure millitor

FIGURE 6B t»0

Fig. 7A (a) Current loop ;!$nal, I., 138 A/div.

(b) Z-coaponent of total Magnetic field,

bz(0,0), 0.58 •aTesla/div . Argon at 0.14 aTorr t*0

Fig. 7B (a) Current loop signal 1^, 13S A/div.

(b) Z-coaponent of total aagnetic field. bz(0.0), 0.58 aTesla/div. Argon at 0.21 •Torr.

2 aa/div.

Pig. 7C (a) Currant loop signal 1^, 138 A/div. (b) Z-coaponent of total aegnetic field, b (0,0), 0.58 aTasla/div. Argon at 0.11 aTorr. 0.8 ~

0.6 r~

0.4

0.2 |-

0

-0.2

-0.4

-0.6

0.8

0.6 6 ms

0.4 |-

Ifl V 0.2 % 0 o -0.2

-0.4

-0.6

0.8 7 ms 0.6 . 0.4 •s Wall 0.2 - 1 1 1 1 ^Vl 1 1 0 2 4 6 ffV^ 10 12 ti1 4 -0.2 - Radius in cm

-0.4 -

•0.6

FIGURE 8 FIGURE 9 (A

o

FIGURE 10 1.0 - 2 ms 4.8 ms 0.8 |-

0.6

0.4

0.2

0 4 6 8 ^W10 12 14 4 6 10 12 Radius in cm -1.2 Radius in cm

-0.4

-0.6

-0.8

-1.0

o u 1.0 6 ms 0.8(

0.6 -

0.4 -

0.2

i i i iVi 0 • 1 | 2 4 6 8\ 10 12 14 -0.2 Radius in ca

-0.4

-0.6

-0.8

•1.0

FIGURE 11 4.8 ms

12 14

o X

(A

0> o> 7.2

6 ms x 3

ill

12 14 14

\s

FIGURE 12 1.0 2 ms 4.8 ns

0.8

0.6, , t

0.4 -

0.2

1 1 I • \ 1 • 0 2 4 6 8 10\ 12 14

0.2 L in cm

0.4

•0.6

•0.8

.1 0 in

M o 7.2 ms

FIGURE 13 1.0 i—

0.5 -

-0.5 -

l.Oi—

0.5 - i o -0.5-

1.1

3.6 ns

0.5- Wall

.•-J I I 1U 10 12 14 Radius in cm

-0.5

FIGURE 14 10

2 ms

5 -

-5 -

j> ms o X a) 4> 4>

FIGURE 15 l.o r-

0.5 U

-0.5 |-

1.0,— 5 ms

}_ in V o.sU^ e ,•

1 1 1 ( 1 1 J o • ^

-0.51--

1.0—.

3.6 ms

0.5|- Wall "4 • ^"*V 1 1 Ts 2 4 6

Z in cm

-0.5|"-*

FIGURE 16 Q Experimental data

Solovev Model

1.0

$ *' \p max "3

FIGURE 17 1.0

Frequency in Hz

FIGURE 18