Design and characteristics of a rotating plasma device

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OF A

ROTATING PLASMA DEVICE

BIBLIOTHEEK TU Delft

P 1937 2268

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DESIGN AND CHARACTERISTICS

OF A

ROTATING PLASMA DEVICE

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE

TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE

HOGE-SCHOOL DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS

IR. H. R. VAN NAUTA LEMKE, HOOGLERAAR IN DE

AF-DELING DER ELEKTROTECHNIEK, VOOR EEN COMMISSIE UIT

DE SENAAT TE VERDEDIGEN OP WOENSDAG 6 OKTOBER 1971

TE 16 UUR

JAN GERARD BANNENBERG

ELEKTROTECHNISCH INGENIEUR

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(Foundation for Fundamental Research on Matter - F.O.M.) with financial support from the "Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek"

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C O N T E N T S

page

**£.b-*.E.I.5.B- — 1 ROTATING PLASMAS 9**

A. Survey of rotating plasma experiments 9

B. Motives for rotating plasma research 12

C. Rotating plasmas in Amsterdam 1't

D. Diagnostics used in Kruisvuur II 20

**£ . t ! . * . P . L L 5 — . i i DESIGN OF COILS AND CAPACITOR BANK FOR THE GENERATION**

OF THE MAGNETIC MIRROR FIELD 2*

Introduction 2|)

A. Capacitor bank 2S

B. Coils with a low number of turns 29

C. Coil design 39

D. Circuit design **

E. Secondary circuits 55

**£.t!.*.E-I.i-5--.lIl OPERATING CHARACTERISTICS OF A FAST GAS VALVE 60**

Abstract 60

A. Introduction 60

B. Fast valve 61

C. Drive unit 62

D. Fast ion gauge 63

E. Valve characteristics 65

F. Density distribution in the vacuum system 70

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page

C.H.A.P.I.E.R..1V ENERGY MEASUREMENTS ON A ROTATING PLASMA 71

Abstract 71

A. Introduction 71

B. Experimental setup 72

C. Operation without insulating pyrex cylinders 76

D. Operation with insulating pyrex cylinders 83

SUMMARY 100

SAMENVATTING 101

CURRICULUM VITAE IO3

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£.y.^.?.I.§.?..-]

ROTATING PLASMAS

A. SURVEY OF ROTATING PLASMA EXPERIMENTS

In 1921, HULL (ref. I) showed that charged particles can move in stable orbits in a region bounded by two coaxial cylinders acting as electrodes and containing an axial magnetic field. Similar arrangements also provide a convenient method of producing rotating plasmas in the laboratory where an applied electric field gene-rates a radial electric current across the magnetic field. BAKER and ANDERSON in Berkeley (ref. 2) suggested the use of the same arrangement for the containment and heating of a thermonuclear plasma in the so-called " H o m o p o l a r " d e v i c e , and BOYER et al. (ref. 3) designed a modified device called " I x i o n " having a central plasma electrode and magnetic mirrors at its ends in Los A l a m o s . Both projects were pu-blished at the Geneva Conference on the peaceful uses of atomic energy in 1958. Our own plans and experiments in Amsterdam originated from earlier work by KISTEMAKER and SNIEDER (ref. k) and turned out to be somewhat analogous to the Ixion device. The Homopolar device is an example of a short disk-shaped d e v i c e , where the cylin-drical electrodes are placed between insulating pyrex endplates and a homogeneous Bfield is directed along the a x i s ; the Ixion device in Los Alamos is c h a r a c t e r i s -tic for the long cylindrical m a c h i n e s . The main drawback of the flat-disk design like Homopolar I and II is that no attempt was made to obtain axial containment and hence eliminate plasma interaction with the e n d p l a t e s . Nevertheless some basic properties of rotating plasmas could be studied. The electric field supplied by connecting a charged capacitor to the e l e c t r o d e s , like in most rotating plasma ex-p e r i m e n t s , ionizes the neutral gas raex-pidly and the ex-plasma rotates at such a drift velocity that all radial forces cancel each other. It was clearly demonstrated that appreciable kinetic energy could be stored and that the device behaved as a hydro-magnetic capacitor. The initial period of high current during which the capacitor

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voltage drops is foliowed by an equilibrium situation between capacitor and dis-charge at nearly constant voltage and negligible current. One is now justified to treat the plasma as a dielectric, remembering that the energy is stored in kinetic form and not by stressing molecular bounds as in ordinary dielectrics.

The capacitor model of the rotating plasma has been verified by the characteristic voltage/time and current/time curves of rotating plasmas, which are typical of the discharge of one capacitor in a capacitor with a leak resistance in parallel. The series resistance of the circuit and plasma is chosen sufficiently high to cause rapid dairying of the current oscillation. If the rotating plasma device is short circuited by a "crowbar", a current pulse is obtained from the discharge of the plasma capacitance. From this useful data on the amounts of energy stored and the storage times can be found. Anderson et al. suggested the use of rotating plasmas as pulse-sharpening devices for thermonuclear experiments. The energy stored in a capacitor bank would be fed into the rotating plasma and then discharged, at a higher rate than would otherwise be attainable, into the thermonuclear machine. LOOMS (ref. 5) has discussed the energy-storage properties of crossed field plasma machines and concluded that the attainable energy densities are small compared with those obtained in conventional capacitor banks, as also are the rates at which ener-gy can be drawn.

Short devices have been operated in Berkeley (ref. 6 ) , Stockholm (ref. 7) and in England by the Central Electricity Research Laboratories (ref. 8 ) . To diminish the plasma losses to the end insulators in the magnetic field direction, three concepts can be fol lowed.

a. The first is the mirror ratio B /B , between the magnetic field strengths B and w — o ' w B at the insulator surfaces and in the midplane, respectively. This ratio is generally involved both in the magnetic mirror reflection process of charged particles and in the loss area at the end walls which is proportional to B /B at a given cross sectional area of the confinement region in the midplane. b. The second is the radial ratio r /r between the axial distance r of a field

o-—w o line in the midplane and the corresponding distance r , where it cuts the

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sur-face of an end wall. The radial ratio determines the efficiency by which the centrifugal force tends to confine the plasma by pushing it towards the midplane when r > r > r .

o w

c. The third method to avoid interaction between the plasma and the end walls is in a transient operation, by the use of the "puffatron" arrangement. Just before the start of the discharge the intended plasma confinement volume is under high vacuum. An electric voltage is applied between the electrodes shortly after a neutral gas blob is introduced into the centre of the device by means of a fast valve. Soon afterwards an electric discharge transforms the blob into a fully

ionized plasma of limited axial intention. During a transient state the plasma is then bounded by high vacuum regions in the magnetic field direction. After some time when the plasma has expanded along the magnetic field lines, an interaction will take place with the end walls. The axial expansion can be delayed by using a magnetic mirror field. The puffatron arrangement can also be placed at one end of the device, and by a suitable arrangement of the magnetic field it can be con-verted into a type of gun system in which the plasma is made to expand axially

into a vacuum region. Ad a.

Examples of long devices where two axial magnetic mirrors are used, are: Ixion at Los Alamos (ref. 3 ) . where the centre electrode consisted of a plasma rod inserted at the appropriate time by means of a fast acting plasma gun, and the experiment in Amsterdam carried out by BANNENBERG et al. (ref. 9) and INSINGER (ref. 10).

Ad b.

The radial ratio is made larger than one in the Homopolar 111 device in Berkeley (ref. 11) using the magnetic field at the outside of a torus shaped coil. This "current loop" configuration has been made still more useful in the Fl device in Stockholm (ref. 12).

Ad c.

The puffatron arrangement was used in Berkeley: the Homopolar IV and V (ref. 1 3 ) . in Ris^ (ref. 1't) and in Amsterdam in the Kruisvuur I experiment (ref. 15) and in

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the Kruisvuur II experiment, described in this thesis. The puffatron as a plasma injector was studied in Livermore (ref. 16) and Berkeley (ref. 17).

Extensive surveys on rotating plasma experiments have been published by LEHNERT ref. 18, 19. 20) and by TOZER (ref. 2 1 ) .

B. MOTIVES FOR ROTATING PLASMA RESEARCH

The reasons for doing research on rotating plasmas can be summarized as follows:

a. Basic Research

By means of the crossed field technique basic research can be carried out on fully Ionized dense plasmas. For the confinement and plasma balance in poloidal magnetic fields, a rotating plasma represents the most general case. The stability problem due to the strong centrifugal force produced by the rotation, was investigated in Amsterdam by BARBIAN (ref. 2 2 ) . This centrifugal force is easily varied by external means and can be used to simulate the effect of a large thermal pressure. It further might be possible to construct special rotating plasma devices in which accurate ex-perimental tests can be made of theoretically predicted values of various transport coefficients In a fully ionized plasma in a strong magnetic field.

b. Cross Field Ionization

Contamination of the rotating plasma resulting from contact with the electrodes and "internal crowbar" along the insulators necessitate the removal of the electric field as soon as a sufficient degree of ionization has been obtained. Therefore a rapid ionization of the gas is desirable. The fast growth of ionization observed in a rotating plasma experiment was studied in Amsterdam by RASMUSSEN (ref. 2 3 ) . The experiments were found to be consistent with impact ionization by thermal electrons, except in certain cases where also ionization by positive ions becomes important.

c. Thermonuclear Fusion and Associated Problems

It is unlikely that rotating plasmas would lead to the realization of a self-sus-tained fusion reactor. This is mainly due to the fact that such plasmas suffer from

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From the technical developments necessary for these measurements we mention: -An improved vacuumswitch, used to switch a peak current of 200 kAmp from a 150 yF

capacitor bank charged to 1't kVolt (ref. 2 5 ) .

-A fast ionization gauge placed in the external neutral gas region to study the gas pressure during a discharge (ref. 2 6 ) .

-A ball-throwing device or ballista, capable of launching a 3 mm glass ball to a given position inside the rotating plasma to measure the rotational energy and density distribution of the rotating plasma (ref. 2 7 ) .

C.2. Kruisvuur I

The original experiment started in I960, was modified in 196't to a device called: Kruisvuur I (Cross fire I) (ref. 15), with a pulsed gasinput and less capacitors. Kruisvuur I was used to study the ionization process in crossed fields for a number of gases (ref. 23) and for the study of the gravitational instability (ref. 2 5 ) . The experiment was stopped early

1967-Meanwhile a completely new rotating plasma device, Kruisvuur II, was built.

C.3. Kruisvuur I I

a. Purpose of the experiment

The purpose of the first rotating plasma experiment (section C-l of this chapter), was to obtain a hot and dense plasma. The E x B method has the advantage that the

ions are preferentially heated in crossed E and B fields and that there is in fact no upper limit, from space charge effects, to the plasma density. A disadvantage is the essentially needed contact of the plasma with electrodes.

The thermal energy of the ions is directly connected with the energy W of an ion in the Larmor orbit. As the energy derived from the potential field is in first instance equally distributed between Larmor motion and drift motion (chapter IV), we find for the Larmor energy of an ion:

2 E^

U = i m v j = j m — J . (') B

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So an obvious way to reach a high ion energy Is to increase the applied voltage. However, the Larmor radius, given by:

should always be much smaller than the interelectrode distance. This condition sets a lower limit to the magnetic field, otherwise a magnetron-1ike discharge develops and a newly ionized particle hits the wall to readily.

From the two equations given above it follows, that - for a given electrode confi-guration - a fourfold increase in the applied voltage, together with a twofold in-crease in the magnetic field, leaves the Larmor radius unchanged, whereas the ion energy does increase with a factor of four.

It soon became clear however, in the first experiment, that one of the limitations in reaching the goal of a hot plasma is the internal breakdown along the insulators. This breakdown sets a limit to the voltage that can be applied and therefore to the plasma energy that can be obtained.

Another problem that presented itself was that the discharge was found to be large-ly independent of the initial gas pressure. The explanation for this unexpected result is that large quantities of gas, H. as well as impurities are liberated from the large unbaked copper electrodes and the insulating pyrex discs, dominating the gas content origionally present.

It was therefore decided to build a new device if possible without the drawbacks of the former one, with the same purpose: the production of a hot and dense hydro-gen plasma.

Several improvements over the first device were realized to overcome the internal crowbar and degassing problems:

-A pulsed gas input is used rather than a system with a homogeneous gasfilling; -No insulating material is present in the magnetic mirror throats;

-The device is mildly bakeable to reduce degassing and the base pressure is in the -8

10 Torr region without organic components in the restgas.

A cross section of this device is given in fig. I; a photograph in fig. 2. A schematic diagram is fig. 1 of chapter IV.

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Fig. 1. Cross section of Kruisvuur II. Only the -right half of the device is draun;

a few flux lines are indicated.

b. Magnetic field

The magnetic field is much stronger, allowing in principle for an increase in the applied electric field and ion energy, without affecting the Larmor radius.

One extra coil placed behind each of the two mirror throats brings the intersection region of the field lines with the cylindrical stainless steel wall to a large dis-tance (60 - 75 cm) from the central region where the plasma is formed in the 16 cm diameter vessel. The intersection region can optionally be covered with a pyrex insulator, to study the influence of endwalls on the discharge (chapter IV, parts C and D) .

The coil construction allows a risetime of the magnetic field to a maximum of -2

2.'t Wb m either in 100 (jsec or 1.2 millisec. Plasma experiments however, were only done in the "slow" mode of operation. The faster risetime would allow for some

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Fig.2. Kruisvuur II. From left to right: pyrex crosstube and coil system.. Background: backside of control panels.

Foreground: vacuum panels. Ceiling: copper tubes to measuring cage at right.

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plasma compression, but the necessary thin walled vacuumvessel (wall thickness 0.1 mm) presented some technical difficulties.

The power supply for the coils consists of a 100 kJoule 2.5 kV capacitor bank, switched with 48 main ignitrons and crowbarred at maximum current with 'i8 crowbar igni trons.

Details are given in chapter II and in part B of chapter IV.

c. Vacuum system and pulsed gas input

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The vacuum system has a basic pressure of 10 Torr, two orders of magnitude lower than the oil-diffusion pumped Kruisvuur I device. At the time of construction (l96'i) it was the first ion pumped system in the institute. Some details are given in chapter III and in part B of chapter IV. The system consists of a 170 cm long stainless steel tube, diameter 16 cm serving also as the outer electrode. The tube can be heated up to 100 C by passing a current of 'lOO Amp, 50 Hz through it. At each end a pyrex cross tube (fig. 1) with six branches is connected, sealed with indium wire. At the two cross tubes ion pumps (100 1/sec and 25 I/sec, respectively) and a titanium sublimation pump are connected. The system is pumped from one atmos-phere by sequential pumping with four sorbtion pumps.

The central electrodes are supported from flanges attached to the insulating pyrex crosses and contain a fast valve at their end (ref. 2 8 ) . The fast gas input system is treated in chapter III.

d. Electri c field

Each of the two central electrodes can be switched with an ignitron to 5 (or less) capacitors (7-7 vF, -18 kV m a x ) ; the discharge can be crowbarred with another set of ignitrons. The series resistance of 0.16 ohm (see fig. 1, chapter IV) is made from a long stainless steel strip, 10 cm wide and 0.1 mm thick, folded in a zig-zag shape with mylar insulating sheets between the folds; this gives a very low

self-induction. The resistance is introduced to damp the circuit In order to prevent oscillations in the current and voltage during the ionization phase.

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e. Measuring equipment

All measurements are recorded on double beam oscilloscopes equiped with Polaroid film cameras, inside a double screened measuring cage. The outer cage is extended

with copper tubes and copper mesh shielding around the 50 ohm coaxial measuring

cables towards the experiment; from these extensions only one is connected to the outer electrode in order to prevent loops. The outerconductors of the coaxcables are free from both cages, and are directly (or via an integrating circuit or a filter) connected to the oscilloscopes. The equipment inside the cage is fed from

a three-phase motor generator set with an insulating shaft; the generator being at the inside, the motor at the outside of the cage.

All the time delay and trigger units are outside the cage, the experiment is started from inside via a flashlamp and fotodiode coupling, whereas the oscilloscopes are

triggered from the timing system again via a light coupling. All these precautions are necessary to obtain cleai. noise free signals, often in the millivolt range, in the presence of large fast rising currents and the associated electromagnetic stray

fields.

D. DIAGNOSTICS USED IN KRUISVUUR II

The voltage over the discharge is measured with a capacitive voltage divider with a

bandwidth from 50 Hz till 6 MHz; the current with a Rogowski coil around the central

electrode and an integrating network. Plasma energy is derived from diamagnetic loop measurements; see Chapter IV, part D.2. The current path inside the vessel is studied with wallprobes; see Chapter IV, part C.I.

A short review of some of the measurements not given in Chapter IV, is given here.

a. Microwaves

A 't mm microwave interferometer setup was used to measure the plasma density in the

central plane. The density measured is above the cut-off frequency for waves of

75 GHz from very early in the discharge cyclus till 300 usee after the start. This 1 9 - 3

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IV, part D.5. where a density of 7 x 10 m i s derived at 32 usee after start. Density measurements for such a high density could be performed much better with a laser interferometer as was done by Rasmussen (ref. 15). A shift of about two fringes for a He-Ne laser interferometer working at a wavelength of 3.39 ym can be expected in our case.

b. Mass analysis

The desorption of adsorbed wall material was studied with a quadrupole mass filtre mounted at 'tO cm from the centre of the rotating plasma in the midplane (ref. 2 9 ) . The desorption of gases from the wall and their subsequent adsorption is studied by taking mass scans at 30 millisec and 15 seconds, respectively, after the dis-charge.

A clean up by a factor of five can be reached in about twenty shots after the sys-tem has been open to the atmosphere. A release of neutral hydrogen from the plasma is found at about 900 usee after the start of the discharge; this time is diminish-ed to '«00 usee if the electric field over the plasma is taken away by an external crowbar.

c. Image convertor camera

End-on photographs with an exposure time of 10 nanosec were made with a Beckman-and Whitley image convertor camera. No flute instabilities were observed.

d. Spectroscopy

With a Hilger medium quartz spectrograph photographic spectra between 7000 A and 2200 A were taken by a lens and mirror system. The observations were done nearly parallel to the axis of the rotating plasma at three locations: near the central electrode, near the wall and in the region between the coaxial electrodes. Near the electrodes impurity lines like Fe.. and Cr . are found as well as the Balnner lines. In the annular space between the electrodes at R = 5 cm the lines of Si..,, Si..., Si , 0. , 0 , B . and B., are found to be rather strong.

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REFERENCES

1 HULL, A.W. (1921) , Phys.Rev. _[8, 31.

2 BAKER, W.R., ANDERSON, O.A. (1958), Project Sherwood (ed. by A.S. Bishop),

Addison-Wesley, p.128.

3 BOYER, K., HAMMEL, J.E., LONGMUIRE, C.L., NAGLE, D., RIBE, F. and RIESENFELD,

W.B. (1958), Proc.Sec.Intern.Conf.on the Peaceful Uses of Atomic Energy,

United Nations, Geneva, Vol.3_l_.

319-ll KISTEMAKER, J. and SNIEDER, J. (1953), Physica 22. 333. 't't't.

5 LOOMS, J.S.T. (1962), Gasdischarges and the electricity supply industry

(Buttersworth).

6 ANDERSON, O.A., BAKER, W.R., BRATENAHL, A., EURTH, H.P., ISE. J., KUNKEL, W.B.

and STONE, J.M. (1958), Proc.Sec.Intern.Conf.on the Peaceful Uses of Atomic

Energy, United Nations, G leva. Vol. 32^. 155;

C H A P T E R I I

DESIGN OF COILS AND CAPACITOR BANK FOR THE GENERATION

OF THE MAGNETIC MIRROR FIELD

INTRODUCTION

The magnetic field to be used in the rotating plasma experiment must be strong

enough to contain the plasma. The ratio of plasma energy density and magnetic

ener-gy density Is called B; B has to be much smaller than one.

An equivalent condition is given in eq. (lOb) of chapter IV:

B'' > 4 u„ E^(mn)

\n ^ .

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— o max a

For: E " 2 . 10 V/m, obtained by deviding the applied voltage of 10 kV by the

-2 20

5 . 10 m interelectrode distance; m equal to the mass of a proton; n - 3 • 10

m and: In — « 1, we arrive at:

8 > 0.56 Wb m"^ .

The Larmor radius is given by:

From this a Larmor radius of: 7 . 10 m is found for a proton subject to the

fields given above. This is small in comparison to the interelectrode distance of

5 . 10"^ m.

-2

The field in the central region was chosen at 1.2 Wb m . With a mirror ratio of 2

-2

the field inside the coils must be 2.'t Wb m . The radius of the central electrode

(0.022 m) is given by the space necessary for the fast acting hydrogen valve

(chapter III). The outer electrode has a radius of 0.08 m and serves also as a

vacuum vessel (chapter IV, fig. 1 ) .

The mean radius of the coils is accordingly chosen at O.IO m, the mean length is

0.21 m. To extend the path length for neutral gas released from the fast valves in

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the mirror throats, to the place where field lines cross the outer wall, two extra

coils are provided. All four coils have the same dimensions to simplify the design.

The spacing between the two central coils is chosen such as to give the required

mirror ratio for the central region. The spacing between the central coils and the

outer coils can be chosen in such a way, that the flux tube tangent to the outer

electrode in the centre does not touch the outer wall between central and outer

coil.

A. CAPACITOR BANK

A.l. General considerations

A convenient way to supply the energy for a magnetic field of short duration (less

than 10 sec), is to use a charged capacitor bank as an energy storage (fig. 1)

and to transfer the electrical energy to magnetic energy by closing the switch S..

If the risetime of the magnetic field is made short in comparison to the field

Si R

1 Fig. 1. Schematic diagram for energy transfer from charged capacitor to magnetic

coil by closing switch S at t and

S„

at

t„,

respectively.

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diffusion time, a plasma can be compressed by the rising field. In this way it is

in principle possible to insulate a plasma from an outer wall and/or to heat a

plasma by adiabatic compression. Once the maximum field is obtained, the field can

be kept at a reasonable steady value by closing the "crowbar" switch S,; in the

shorted coil the current then decays with a time constant given by LR . A rough

estimate of the required electrical energy can be found from the magnetic energy

density integrated over the volume. If we assume that the magnetic induction of

-2

2.'t Wb m fills a cylinder of radius 0.10 m and length l.'t m, we find for the

total magnetic energy:

2 T ^ — T r r ^

i=

100 kJoule . (3)

2 ^-o

This estimate neglects the stray field outside the coils, however, this is

compen-sated for by the assumption of a homogeneous field inside the cylinder.

A . 2 . Choice of parameters

The cost of a capacitor bank for a voltage below 20 kV, is mainly given by the

energy content and not by the voltage. Reasons for choosing a high operating

volt-age can be: the achievement of a fast growing magnetic field if a reduction in

self-induction of the coil is not convenient or possible. In our ease a moderate

risetime of 100 usees was considered adequate, so the voltage level can be chosen

2 rather low. An efficient transfer of electric energy 1/2 CV in magnetic energy

2 1/2 LI requires (see fig. l ) :

(a) a low self-induction of all components in comparison to the coil

self-induc-tion;

(b) the sum of all resistances R in the circuit to be low in comparison with

/ LC to reduce damping.

If these conditions are fulfilled, the current upon closing S. at t. = 0 is given

by:

I = V / | ^ s i n — L - (t, < t < t j ('t)

^

rcc

1 - -

2

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t2 = f /Tc- (5)

The phase angle between voltage and current is nearly 90 , so the capacitor voltage

is zero at t- and all the energy is transferred to the coil. On this moment S. is

closed and the current through the coil decays exponential:

I . V /Pexp(- -^ t) . (t > tj) (6)

The choice of suitable switches for S and S_ depends on voltage, rate of current

rise, maximum current and total charge. Both switches must hold the full voltage

without prefire, whereas switch S- has to close at a very low voltage and must have

a low resistance. The rate of current rise in a switch is limited by the formative

time of a conducting path and self-induction effects. The current carrying capacity

depends on mechanical forces and pinch effects. The total charge that can be passed

is dependent on electrode erosion.

For the time scale we are considering, switches depending on some means of plasma

formation like spark gaps, vacuum switches, ignitrons and solid dielectric switches

are possible, whereas mechanical switches are too slow.

From eq. ('t) we find for S. (start switch):

(f) = ^ att = t, (7)

max

W = V / T at t - t2 (8)

I dt = C V (9)

*1

From eq. (6) we find for S. (crowbar switch):

(^)

-^

a t t = t , (10)

max

I = V / | " at t = t, (11)

max L

i

j I dt = CV (1 v'^ï^) (12)

^2

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The circuit quality is defined as;

= ;/r.

0 = ^ / ^ . (13)

Comparing the demands for the start switch and the crowbar switch, we note that a l -though the peak currents are the same, the rate of current rise and total charge are vasty different. In this simplified circuit without any inductance in the path of S_, the current rise is unlimited; in a practical circuit this is not the case. The total charge passing through S_ is a factor of Q (circuit quality) higher than the charge passing through S..

We now ask: what happens if we choose an operating voltage:

V, = aV (111)

instead of V , while keeping the v o l u m e , the amplitude and time scale of the m a g n e -2

tic field constant? The magnet c energy is not changed, so 1/2 CV is unchanged, -2

so: C. = a C From eq. ('t) and the condition that the time scale is invariant it follows that / LC is unchanged, so: L = a L. Such a change in self-induction can be obtained by increasing the number of turns n to: n. = an. For a coil of given dimensions with a constant filling factor, the coil resistance will go from R to:

2

R, = a R, if skin effects can be neglected, so the time constant given in eq. (6)

-2 2 2 remains also unchanged. Substitution of: V = aV, C. = a C, L. = a L and R. = a R

in eqs. 7 " 12. reveals that an increase in the voltage with a factor a, decreases the burden of both switches as far as current, current rise and charge is concerned, with a factor a

The capcitor voltage we did choose was only 2.5 kV. The analysis given above indi-cates that a voltage level of say 20 kV, would be a better choice as far as the switches and capacitors are concerned. This rather low level was chosen, however, because at the early stages of the design we were considering the use of simple, un-shielded one-turn coils inside the vacuum system. The vacuum system would then be immersed inside large ('t'l cm internal diameter) D . C operated c o i l s .

The 100 kJoule capacitor bank contains 96 capacitors o f : 320 uF, 2.5 kV (Bosch type KO3GH't02). These capacitors are made of a number of metallized paper rolls

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arranged in a metal case filled with insulating grease. The metal is vacuum evapora-ted on the paper on one side, with an uncovered strip on one edge of the paper. Two of such metallized strips with an insulating centre strip, are rolled together; end contacts are provided by metal spraying of the two end faces, giving a very low in-ductance connection. In cases where a pinhole in the dieleetricum leads to a short. the available energy easily evaporates the metal without burning the paper. In such a way the insulation is restored without any further damage. The self-1imiting and self-healing properties make it possible to connect large numbers of these capacitors

in parallel without any danger for an explosion due to the feeding of one defective capacitor by all the others.

The bank is divided into four units, each one feeding one coil. The self-induction of the coil for a risetime (eq. (5)) of 10 sec and a capacitance C = l/'t . 96 . 320 uF, has to be: L = 0.5 uH.

The self-induction of a coil with small radial thickness is given by: 2 D 2

U n 7T R

L = K - 2 - ^ (15) with R = coil radius, I = coil length, n = number of turns. Coil radius and length

are adapted to the outer electrode dimensions (see introduction).

The value of K is tabulated by ROSA and GROVER (ref. 1 ) , as a function of: £R . For R = 0.1 m, £ = 0.21 m we find: K = 0.67. The required self-induction is obtained if we choose the number of turns: n = 2.

B. COILS WITH A LOW NUMBER OF TURNS

B.l. General considerations

A coil with only two turns can be made from two layers of sheet wrapped around each other with a common axis, or from two turns proceeding in the axial direction. In both cases severe asymmetries in the field, due to the current connections to the ends of the sheet windings do occur. This is undesirable because of the bad in-fluence on the plasma containment. Moreover, the mechanical forces are difficult to handle and the self-inductance of the coil connections is not small in comparison to the coil induction.

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Fig. 2. Sketch of a two layer coil with a number of turns n < 1 and with m

paral-lel strips. The pitch angle is a.

These drawbacks are eliminated by constructing the coil out of a number of m paral-lel strips (fig. 2) instead of having only one strip. The m strips lying on a cylindrical surface are fed axially from one side; the current in each strip is I m"' where I is the total current fed into the coil. In order to return the cur-rent with a minimum of extra inductance, the coil may consist of two such layers. One end of the coil is then used for the current feeding; at the other end the strips of the inner layer are bend around to the upper layer. Coils of this type were developed independently in Garching (ref. 2 ) , in Los Alamos (ref. 3) and in Amsterdam by BANNENBERG and INSINGER. A much more advanced design was used in Cul-ham Laboratories in 1967 (refs. 't, 5 ) . The feeding should be arranged in such a way as to leave enough space for the magnetic flux to close around the outside of the coil upon itself, without too much hindrance of conducting material. The number of strips (m) can be chosen arbitrarily. It is convenient however to feed each strip by the same number of capacitors. In that case metallic connections between the parallel strips can be avoided if for each strip a separate switch and capa-citor arrangement is used. In our design 2't capacapa-citors feed one coil; as a number of strips we have chosen: m = 12.

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c

m r t 2 n = 2 p = 1

Fig. 3. End-on view of three coils with a number of turns n and with m parallel strips. Capacitors can be connected between the leading part of strip number 1 and the end of strip number p.

The number of turns: n is given by the number of times that each strip encloses the flux. Fractional n numbers can readily be obtained, although in that case it may be necessary to connect the capacitors between the leading part (a) of one strip and the end (b) of another strip. Fig. 3a gives a schematic view of a coil with n = S/'t, m = 12 where the capacitors can be connected between a,-and b . ; a . and b - , e t c . In general we can w r i t e for the C-angle between the leading part of the first strip a, and the end b of the p strip:

0, = n 2 -1+ (p-1) — (16) Ip m

wi th 1 < p < m.

By choosing a suitable p number, w e always can arrange this angle to be near zero or a whole number of 2TI from zero. The capacitors are then connected between a^ and b : a, and b , and so on in cyclic order. A classical O-pinch has m = 1, n = 1 and

p 2 p+1

p = 1. In the Carridi 0-pinch (ref. 6 ) , a solution with m = 6 and n = 1/6 w a s chosen, with p = 6 (fig. 3 b ) . T h e Carridi coil however has the classical sideway feeding and uses only one layer.

a

nn=12 n =3/4 p = « m : 6 n = 1/6 p=6

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The Culham design (ref. 5) uses m = 1 0 , n = 1.1 and an annular collector does con-nect the ten strips in p a r a l l e l .

B . 2 . Kruisvuur II col Is

Our own design has m = 12, n = 2 and p = 1 (fig. 3 c ) . The pitch angle a (fig. 2 ) , is chosen to be: a = arc tg -r—^. leading to a = 18 'lO' for £ = 21 cm and R = 10 cm.

2TTR

The same pitch angle was chosen in both layers. Consequently the strips proceed in the 0 direction over an angle somewhat larger than 2TT in the inner layer and some-what less than 2ii in the outer layer due to the difference in the circumference of both layers. The width available for one strip is: sin a "• 1.7 cm. To allow

m

for insulation between two adjacent s t r i p s , a space of 0.5 cm is necessary, leaving a strip w i d t h of 1.2 cm. The strip thickness is taken as 0.5 em to give the re-quired strength. The spacing in radial direction between the two layers is also 0.5 cm.

The useful field in the axial direction B is set up by currents flowing into the 0 d i r e c t i o n . We will now calculate a general expression for the I current. We call: n » the width of copper strip devided by the width of copper strip plus insulation

5irR

(n • filling f a c t o r ) . Then the strip width in the z direction is: n tg a. In each strip a current — is flowing. So the current density for current flowing in 0 direction in each strip is:

1 -•oS ' 2ïïR

n ^ ; p tg a

The current density for currents flowing into 6 direction in the insulation between the strips is: j . . » 0.

So if the current density j c 's spread over the width of strip and insulation the overall current density in 6 direction becomes:

Je -

" hs

' 2.R tg a

^°'

""'^ '"^"^- <'^'

As can be seen from fig. 2 the coil length can be expressed in the number of turns n, the radius R and the pitch angle a:

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The total current encircling the axis in the two layers can be found from eqs.(17) and (18):

Ig - 2jg £ - nl. (19)

The current I and thus the useful * flux is seen to be independent on R, £, m,

a and n.

B.3. Self-induction

The self-induction is by definition: nt

L - - ^ . (20)

Substitution of eq. (19) gives: n 4

L = - T - ^ (21) 8

with I the total current encircling the axis.

From eq. 21 it follows, that the self-induction of a coil like the one in fig. 2 can be derived from the self-induction of a simple one turn e-coil by multiplying with n (see eq. (15)); n can be any number, also a fractional number.

B.'t. Leak self-induction

The total current I flows from the left end of the coil to the right end into the inner layer and then back again to the left into the upper layer. So in both layers

1 = 1 (22) The current I is like I independent on R, £, m, a and n.

z 6 The field created by I is:

for r >^ R. where R is the layer radius. Inside R, the B field is zero. For the u I

second layer we have B, = - -, for r > R, and inside R, this field is zero. The

8 27rr — 2 2

t o t a l B f i e l d f o r a two l a y e r c o i l is t h e r e f o r e i d e n t i c a l z e r o inside the f i r s t

8

layer and exactly compensated outside the second layer. So there only exists a B 9 field between the two layers. The coupling between the total current I, which

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en-circles the flux * once, gives rise to a leak self-induction. For an interlayer 6

spacing Ar we have:

*e

=

I T R

• "^

• (2'')

The leak self-induction is therefore:

\-l'-T^ •

(«)

The ratio of the leak self-induction to the coil self-induction is found

^ = - ^ ^ 2 ^ - ' . . 10-3. (26) coil K2Ti^R-'n

B.5. Strip self-induction

We will now consider the self-inductance and mutual inductances of the strips in some more detaiI.

In a 8 coil made from one sheet of conducting material, the current density can dis-tribute itself in such a way that no flux can penetrate the coil material if the field rises fast enough. In the type of coil we are considering here, the redistri-bution by eddy currents is limited to the strip dimensions. So there is a flux leakage between the strips, unless special precautions like a varying pitch angle a

near the coil ends, are used. Because of the flux leakage, the coupling factor be-tween the strips is less than one. We will call the strip self-inductance L , which

'^ s is the same for each strip because of the m fold symmetry of the coil. The coupling

between the strips is dependent on their relative position and will be called: k ., k.,, k-, ..., the subscript refers to the strip numbers between which the coupling factor is taken. If the m strips are numbered in cyclic order we have:

^ 2 = S m • ^ 3 ° ''l(m-l) " ^ • ' "»^e°^e^:

If all the m strips are in parallel and we have a total sinusoidal current I, the current In each strip is Im . The voltage over each strip will be the sum of the self-induction voltage and the induced voltages due to the current in all the other

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strips. So:

V = Im^^uiL^ + k,, .^L^ + k,,u;L^ + . . . + k, ioL ) (27)

s Iz s IJ s im s •

If we call the self-induction of the coil with m parallel strips L we have:

^

'^ par

V = I .Lp^^ (28)

Combining eq. (27) and eq. (28), gives:

"-n^r = "-ï ""'' (1 + k + k + ... k. ) . (29)

par s 12 13 Im

From eq. (29) we conclude that the coil self-inductance is smaller than the strip

self-inductance for coupling factors smaller than one.

If all the m strips are connected in series and again a current I is flowing into

the coil, the voltage over the first strip is:

**V, = l(u.L^ + k,2'^Ls* ''U'^^s* ••• * h m - L s ' .**

over the second

V, = I(uL + k-,uiL + k.,ujL + ... + k. uL ) .

i.

s z I s

l i s

Zm s

Because of the symmetry relations between the k's, we find for the total voltage

over the series connected coil:

V = ml (uL + k,,u)L + . .. + k, uL ) . (30)

s I / s I m s

For the series connected coil we have:

V = 1 Ü.L . (31)

series •

Combining eq. (30) and eq. (31) gives:

L = mL (1 + k,, + k,, + ... + k, ) . (32)

series s 12 13 Im

Regardless of the coupling between strips, we see from eq. (29) and eq. (32) that

2 there is a factor m involved in going from parallel to series connection. This fact

enables one to measure the rather low self-induction of the coil more accurately

and can be used to increase the risetime of the magnetic field with a factor m.

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B.6. Radial coil forces

The maximum current in a coil is given by eq. (8); with V = 2.5 kV, 2'i capacitors of 320 uP per coil and L = 0.5 uH, this current is I = 310 kAmp. The maximum radial forces occur, if all four coils are arranged on one common axis close to-gether to form an almost uniform field with 't n turns over a length of 4 £. The B field in the coil centre is then given by:

y nl

B^ = - \ - - 3.7 Wb m '•. (33)

For a single coil the field is lower by a factor K = 0.67 given by ROSA and GROVER (eq. (15)).

The associated magnetic pressure is: B ^

P = ^ . (34)

Substitution of eq. (33) into eq. (3't) gives:

2 T 2

U n I c -9

p = -. = 55 . lO' Nm "• (35)

2£''

this is the pressure working on the inner layer.

The outer layer is immersed in a B field of about half the centre value, so the 5 -2

pressure is: l/'t . 55 . 10 Nm .

The B„ field between the two layers is given by eq. (23); the magnetic pressure ac 8

cording to eq. (3't) is therefore: ,2

p - — ö - 1.5 . 10' Nm . (36) 2(2ïïR)''

The maximal radial pressures are (eq. (35) and (36)): Inner la^er: ' 2 " 2 Pi = - ^ { ^ ^ - l = 53.5 Nm'^ (37) Outer layer: p„ = ^Ar- { - ^ * ^ } = 15.25 Nm-2. (38)

^

k-J

(2.R)^

(34)

by arranging the dimensions so, that the part between brackets in eq. (37) is zero.

The criterium one finds is: £ = n2-R.

Substitution of eq. (l8) gives for the force free case:

tg a = 2 (39)

For a pitch angle a larger than this, the inner layer is subject to an inward

pres-sure.

B.7. Axial coil forces

Axial coil forces find their origin in the local radial component of the magnetic

field B and the current flowing at a right angle into the 8 direction. The B

com-ponent for r = 0.1 m is strongly z dependent. If we consider only one coil, we have

B = 0 at coil centre: z = 0 and B reaches a positive, respectively negative maxi-mum at the two c o i l e n d s : z = ^ 0 . 1 0 5 m .

The total axial compression force in the z = 0 plane of the coil is:

A>ial Force

1^. 10^ (Newton)

10

-ZClTWlM-)

Fig. 4. Graph of radial magnetic field B = f(z) at a radius r - 0.1 m for a

cytin-6 ~1

der coil (see insert) with a

8 current of 2 . 10 An . The axial force due

to the Lorentz force is integrated in 0. 003 m steps and given in the graph

F = f(z).

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£/2

F = 2Ttr j ,

ax 5 B d z

CO)

w h e r e the coil is treated as a c y l i n d e r w i t h radius r = 0.1 m and length i = 0.21 m w i t h a c u r r e n t d e n s i t y jg = ' T = ^ . 1 0 ^ A m " ' . V a l u e s of B^ = f(z) at r = 0.1 m are c a l c u l a t e d w i t h : " T a b l e s of Semi - Infinite C i r c u l a r Current S h e e t " (ref. 7 ) . T h e result is g i v e n in f i g . 't. T h e v a l u e of B^ g o e s to infinity at z = 0.105 m , t h e r e -fore w e take the B v a l u e for z = 0.10't m a l s o in the interval O.IO't m _< z _< 0 . 1 0 5 m. T h e c u r v e B = f ( z ) is integrated g r a p h i c a l l y w i t h steps of .005 m and m u l t i

-COILI

SPACER COILI

Fig. 6. Radial magnetic field at a radius of r ^ 0.1 m and axial forces for two

coils I and II with the sane dimensions and currents as in fig. 4 at a

coil spacing of 0.12 jriezer.

a) Magnetic field due to coil I (fully draiy.) 3nd xV. II (dashed line);

b) Super position of magnetic fields;

a) Axial forces due to ceil I (fully dra.--.) ar.d coil II (dotted line);

d) Super position of axial forces.

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plied with 2i'r j , to find the axial forces in the coil as a function of distance

(see fig. 't). The maximum force amounts to 11.2 . 10 N in the midplane of the coil.

If a second coil is placed on the same axis at some distance, the field of coil I

extends in the region of coil II and vice versa, see fig. 5a. To calculate the

for-ces, one can use the resulting radial fields as sketched in fig. 5b, or one can

calculate the extra forces due to coil II and use the superposition principle. We

used the latter method and found an extra axial force at the end of the coil I of 2.2 . 10 N for a coil spacing of 0.12 meter, fig. 5c. This force has to be

taken up by the spacer (fig. 5 d ) . The axial compression force in the neighbourhood

of the coil midplane is only increased with O.U . 10 N, due to the rather steep slope of the force curve. The 't coils are prestressed with 6 heavy bolts with a

total force of 10 ton, to prevent a rebounce of the coils as the magnetic

compres-sion force falls away.

The spacers between the coils are made from araldite with a quartz powder filling.

The end faces of these hollow cylinders are turned on a lathe to ensure parallel

end faces.

C COIL DESIGN

C I . Coil construction

The large forces involved necessitate a strong coil construction, whereas the use

of metal parts in the neighbourhood of the fast rising magnetic fields must be

avoided. In cooperation with the Avio Diepen plastics division, a construction with

glass tape and araldite was chosen. The coil was built up step by step on a

slight-ly tapered steel cylinder. The cylinder could be mounted in a simple frame with its

axis horizontal and rotated around by hand. On one side of the cylinder there is a

flange with 2 x 12 radial slots, formed by a number of demountable blocks. The length of the cylinder is about 2.5 times the coil length, this is necessary to

take up the excess length of the copper strips in winding the first layer.

The fabrication process is now as follows:

(a) The steel cylinder is sprayed with "Slip-Spray" to ensure no bonding between

(37)

(b) A 1" w i d e glass tape runs over some pulleys through a small vessel filled with araldite and is wound tightly on the steel cylinder. A total thickness of 6 mm is w o u n d , this is wrapped with a thin polytheen foil and then a nylon rope is wound over the foil to squeeze out any superfluous araldite. The whole cylinder is then baked overnight at 80°C. The glass araldite cylinder is turned on a lathe to the required dimension (5 mm wall t h i c k n e s s ) .

(c) Now the twelve copper strips are prepared. Each strip is 1.5 m long with a 5 X 12 mm cross section. The last 20 cm on both sides and the central 20 cm of each strip is first made soft by heating with a gas flame. With specially made tools a length of 15 cm is firstly bend over 90 and then twisted over

o =» l8°'to' with another tool (fig. 6 a , b ) . The 15 cm part is then inserted and clamped in a radial slot of the flange and can be wound with the pitch angle

I8°'t0' over the araldite cylinder. The exact angle is measured by the

intro-uconil lairtr first laytr

Fig. 6. Details of coil construction, dimensions in mn, pitch angle a = 18 40 .

The coil ia drawn unfolded for clearness' sake.

a) coil end strips, top view;

b) coil end strips, bending and twisting method;

a) other coil end, top view;

(38)

duction of a sheet of paper with a number of parallel lines drawn under the required a n g l e , between the cylinder and the windings. After the twelve w i n -dings are wound, they are clamped with a few steel strips; the paper is re-moved and small 5 mm thick spacers are used to equalize the gaps between the copper strips. The strips are now soaked in araldite over the length of the underlying araldite cylinder and the whole assembly is baked again at 80 C

in the oven. After this the spacers are removed.

(d) The 5 "HU wide helical gaps are filled with a silicone rubber; this acts like an incompressible fluid and equalizes the magnetic forces. So, even if the binding between copper and araldite were not perfect, the windings are preven-ted to move into the axial direction due to the silicone rubber. The forces in radial direction are taken up by glass tape and araldite. The silicone rubber is baked and the excess material can be cut away with a knife.

(e) The strips are now covered with a 6 mm layer of glass tape and a r a l d i t e ; this is baked and turned on a lathe to a thickness of 5 mm as was done in step b. (f) The length of copper strip for the second layer is now unwound from the steel

cylinder, one strip at a time. The strip is bend with a pair of tools out of the plane of the first layer and folded over to the plane of the second layer (fig. 6 c , d ) , in such a way that in this second layer the pitch angle is again l8°'t0 . In all four coils the copper helices are right handed in the first and left handed in the second layer. The end of the strip is bend over 90 and twisted over I8°'t0 (fig. 6a,b) and can then be clamped in the appropriate slot of the flange. The location of this 90 bend has to be measured carefully be-cause the bend has to be made before the strip is fully wrapped around the cylinder. The rest of the procedure is as in step c, d and e; the only differ-ence being that the total thickness of glass tape and araldite wound on the second layer is > 16 mm to give added strength for radial forces.

(g) The endface of the c o i l , where the strips extend radially, can not be wound with glass tape. Instead the space is filled with roving (glass fibres of a few cm length) and araldite. Finally, the end clamps are removed and the cylin-der is withdrawn with the aid of a few hammer blows.

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C.2. End connections

Both ends of each strip are parallel to each other at a 5 mm spacing and protrude radially out of the coil (fig. 6a.b). Soft soldered to the strips are brass sector shaped blocks (fig. 7 ) . There are twelve flat blocks soldered at one edge to the strip ends from the first layer; these blocks are all arranged on one circle at the front end of the coil. With an axial spacing of 20 mm the other twelve blocks are arranged also on a circle. These blocks are L shaped, the short legs of the L are soldered to the strip ends of the upper layer. The flat blocks have two large holes each, the L blocks two smaller holes. Coaxial cables are equiped with cylin-drical aluminium bushes, one ^ 30 mm clamped on the outer braid and one (^ 20 mm on the inner braid. These bushes fit in the holes and are clamped by one side screw. This system, where the bush is pressed against the inside surface of a hole opposite to the side screw over a fairly large surface, is both simple and reli-able for the currents we used. Each coil is fed with 2't creli-ables; it is therefore of some advantage to arrange these cables in such a way, that there are no cables

side screws

L-block

flat-block

7 tapered

spacers

hard soldered

coax cable/

coax cable ^

soft soldered

coil strips

Fig. 7. End connection blocks soldered to end strips. Two large perspex rings, one

behind the L-blocks and one in front of the flat blocks are omitted.

Omitted also are perspex filling blocks between the end connection blocks.

(40)

in the central section of the four coil assembly, where the plasma is formed and radial diagnostic ports are used. This can be done by the use of two " l e f t " coils and two " r i g h t " c o i l s . The coil w i n d i n g s h o w e v e r , have to be the same for all coils to simplify the c o n s t r u c t i o n . So the connection blocks must be made different for the left and right c o i l s . The L shaped blocks w e r e therefore made from two p a r t s , hard soldered together either in a right-handed or a left-handed version. The flat

b l o c k s simply can be turned over to be soft soldered either at the left side to a strip or at the right side. There are two large perspex rings, one in front of the flat blocks and one behind the L b l o c k s , which together with sector shaped p e r s p e x filling blocks in the gap between the brass blocl^s, are bolted together to form one rigid s t r u c t u r e . The bolts go through the whole stack of p e r s p e x ring, flat brass b l o c k , p e r s p e x b l o c k , L brass block and perspex ring. A teflon tube covering the full length of the bolts is used to insulate the bolts from the brass b l o c k s . The 5 mm gaps between the copper strips and between two adjacent blocks

are filled by two tapered perspex s t r i p s ; they are fixed with a hammerblow. Mylarfoil folded around the leg of the L blocks is used to increase the creeppath b e -tween the blocks of o p p o s i t e polarity. The d i s t a n c e be-tween the inside of the rings of blocks and the o u t s i d e of the coil is made large enough to enable the cables for the second coil to pass this annular space in the first coil.

C.3. Mode of o p e r a t i o n

The coils can be operated in two different modes of o p e r a t i o n . The first one is with 2't coaxial cables inserted in the coil end c o n n e c t i o n s . The 12 strips are then in p a r a l l e l . The second mode is to connect the 12 strips in series by the in-sertion of brass bridging b l o c k s . These blocks have one (J 20 mm long cylinder and one (f 30 mm short c y l i n d e r ; eleven blocks can be mounted instead of the coaxial c a b l e s . The connection to the capacitor bank is then made with heavy cables solder-ed to brass cylinders that can be insertsolder-ed in the two spare holes in the c o i l . The cables end on the other side on two thick a l u m i n i u m flanges equiped with holes to take up the coaxial c a b l e s .

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the substitution of: L = I't't. L (Itl) series par. * ' and R . » }kk. L (It2) series par. * ' in eq. ('t - 12).

The maximum current is 12x lower, the number of windings is 12x higher, so the B

field reaches the same value. The timescale from t. till t- is 12x longer, the

de-cay rate for t > t. does not change much.

As for the switches, in the series mode of operation switch 1 has to carry the

same charge, but the current maximum is lower (1/12) and the rate of current rise

is much lower (l/l't't); switch 2 has to carry only 1/12 of the current and also 1/12

of the charge. D. CIRCUIT DESIGN

D.I. Ignitrons

For the relatively low voltages we are considering here, ignitrons are very useful

as a switching element (ref. 8 ) . Ignitrons will work down to less than 100 Volt

without the need of any adjustment as is often necessary in spark gaps. This enables

one to choose the value of the magnetic field by an adjustment of the charging

volt-age.

Substitution of: L = 0.5 uH, E = 2.5 kV and C = 2't . 320 uF in eq. (8) gives:

I = 310 kA. There is no ignitron on the market for this high current, so we have _max _- _' _{S 3 .} to take several ignitrons in parallel. With 12 ignitrons in parallel for both switch

1 and switch 2. the maximum current per ignitron is only 26 kA. For this current a

two inch ignitron like: Westinghouse WX 't231 can be used; this ignitron can carry a

peak anode current of 35 kA. The peak anode voltage for this type is 15 kV, both in

forward and inverse direction. The start ignitron has to block the voltage in forward

(42)

ignitron has to block only during the current flow through the start ignitron. The crowbar ignitron is connected in the inverse direction and can only be triggered reliable if the capacitor voltage has gone through zero to a 50 Volt level in the inverse direction. The current take over by the crowbar ignitron will be consider-ed in some detail in the next section.

D.2. Crowbar

We consider the s i m p l i f i e d c i r c u i t ( f i g . 8 ) . where the c i r c u i t resistances are

o m i t t e d , but the s e l f - i n d u c t i o n of cables and i g n i t r o n s are introduced as L, and

Fig. 8. Modified circuit diagram with circuit self-inductances L. and L„ taken into account.

Dashed voltage and current graphs do occur if S„ is not triggered at the right nom.ent.

(43)

L-. The coil with associated cables if represented by L,.

At t = t. ignitron S^ closes, and a sinus current starts to flow with a maximum

value at t » t,:

/=X

1 max c L. + L.^

(43)

During the time t^ - t^ the capacitor voltage decreases in a cosinus way; this

voltage is zero at t = t, if there is no resistance in the circuit.

If now at t = t. the switch S. is closed, the self-induction as seen by the current

I, decreases due to L, being now in parallel with L,. The period of the oscillation

is accordingly reduced, so

t, - tj = 1 / (L, + Lj) C (44)

and:

-

I ÜJT"

-) C (45)

^ 2 - ^ 3 - l / ^ ^ ^ ^ 3

The self-induction L- is taking over the current gradually with a (1-cos uit) wave

form. If the ignitron S. remains conductive in the reverse direction, then the

dotted curves in fig. 8 will be followed. The load current I, then has a peak value

I as given in eq. (43), with a superimposed ripple amplitude:

L,

^ ' (46)

L- + L.. • 1 max

around a mean value:

L,

"3

L. + L 1 max

(47a)

A small ripple on I, can be reached by making the crowbar inductance L^ small in

comparison to the load inductance L,. A much better approach is to prevent a

re-strike of the ignitron S, , because then also the large current in the crowbar

switch amounting to:

2 L

2 max L- + L.. • 1 max

^ — - (47b)

(44)

It is the energy content of the self-induction L . that may prevent a fast enough deionization of S.. In the real circuit the ignitron-, cable- and coi1-resistances damp the oscillatory component of the currents and cause the mean load current to fall e x p o n e n t i a l l y . The triggering of S. can only be successful if the voltage has gone through zero and has reached a value of at least 50 Volt positive (anode to c a t h o d e ) . There are three p o s s i b i l i t i e s :

(a) S- triggered too early. Result: I. does not start. The current 1, goes on o s c i l l a t i n g through the load (dashed line: 1. in fig. 8 ) .

(b) S- triggered too late. Result: I- s t a r t s , but has an overshoot to almost the double value because Ij o s c i l l a t e s . The load current I , decays exponentially but has a small ripple (dashed lines: I., ly and I , ) .

(c) S triggered on right moment. Result: I. starts and has no overshoot. I does not reverse sign but remains zero after t,. The load current I , decays

exponent-ially after t, w i t h o u t a ripple (full lines in fig. 8 ) .

It has to be noted that, if only the current in the load is monitored, it is d i f f i -cult to see the d i f f e r e n c e between the possibilities b and c. The possibility b , where S^ is triggered too late, has to be avoided in any case at the full operating voltage because it may damage the ignitron S- due to the high current. In the actual circuit with resistance damping, only one overshoot occurs because I. does not re-strike another time when 1 goes through zero again at t = t,.

The voltage of the capacitor is proportional to the ratio of the recharging time (t_ - t,) to the decharging time (t. - t - ) . So we find (in the case that S is triggered on the right m o m e n t ) for the capacitor voltage for t > t-,:

/ L L + L L + L L •

^ = ^c ^TLTTTjRi-rrJ) - <'*7)

The influence of resistance in the circuit is visible in fig. 9. where the voltages o v e r the capacity, the circuit resistance and self-induction are given.

These reactances are concentrated here each in one e l e m e n t , in reality there are several se1f-inductances and resistances in s e r i e s . The curves are drawn for a capa-citor C charged to a voltage V, that is discharged in the LR circuit by the closing