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ASPECTS OF ULTRAFAST SPARK GAP SWITCHING

FOR UWB HPM GENERATION

J.M. Lehr, C.E. Baum, W.D. Prather and F.J. Agee

High Energy Sources Divisioq Phillips Laboratory

Kirtland AFB, New Mexico 87117

ABSTRACT

The Air Force is interested in compact ultra-wideband systems which utilize a

minimum volume of high pressure gas. These desires lead us to look closely at single

channel spark gaps, because both the size and volume of gas, for example, hydrogen,

under pressure can be much less than needed for sources containing ring gap switches.

While single channel spark gap switches are desirable, the intrinsic inductance of the

spark gap is prohibitively high to achieve large rates of voltage rise.

For fbture applications, the limit of spark gap technology for ultrafast switching is

explored. Of primary interest is the fastest possible risetime achievable with a single

channel spark gap. Thus fm we have calculated the limit on the achievable risetime

with spark gap technology, using three different approaches, which are all in good

agreement. The first examines the excitation rates in gases to determine its limitations.

The second assumes a streamer mechanism and uses the velocity of propagation to

estimate the achievable risetime. The third utilizes an equivalent circuit model.

It is commonly believed that the impedance mismatch in the spark region, caused by

the additional spark gap inductance, is unavoidable. To reduce the effect of the

intrinsic inductance of the channel, the High Energy Source Division has devised a

simple geometrical alteration to the spark gap geometry which reduced the inductance

per unit length of the spark gap to that of its transmission line feed. This is anticipated

to permit the realization of picosecond risetime UWB HPM sources.

INTRODUCTION

The general limitation on the achievable risetime for gaseous ultra-wideband (UWB) high power

microwave (HPM) sources is the spark gap. It is of interest, for a myriad of applications, to produce,

control and accurately measure ultrafast breakdown in spark gaps. Thus, knowledge of the

fimdamental limitations of spark gap technology is desirable. Three treatments are used to examine

the limits. The first examines the rate of carrier generation in the gaseous insulating media under

uniform field conditions to estimate the minimum time to achieve the critical charge carrier density.

Secondly, the limitation imposed by the finiteness of the electromagnetic propagation. Finally, a

circuit model for the post-breakdown circuit is invoked to derive the limitation on the rate of voltage

rise. These treatments provide insight into ultrafast breakdown and guidelines for its generation.

U.S. Government work not protected by

U.S. copyright.

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Peaking Spark Gaps

Pulse

conditioning systems are being used to generate UWB High Power Microwave (HPM) in the

10’sof gigawatt power range. [1,2] In general, this is accomplished by successively manipulating the

timescale at which energy is delivered to a load. A block diagram of such a power conditioning

systeq is shown in Figure 1. PulseWidths in the sub-nanosecond regime are produced by charging

transmission lines of successively shorter electrical length along with an accompanying increase in

voltage,

Prime Energy

Power

Storage I

‘*

ms ns

Kilowatt ~ Megawatt ~ Gigawatt

Figure 1.

UWB

HPM is produced by radiating high power pulses of very

short duration. Subnanosecond duration pulsed are generated by successively

reducing the timescale at which electrical energy is stored.

The switching element is a major component of any power conditioning system and, for UWB FIPM

generation, ultrafast closing capability, along with fast voltage recovery are desired. A fast pulse

risetime is critical because the risetime contains the high iiequency components of the resulting

spectrum. To sharpen the risetime on a pulse, a spark gap conflguratioq called a peaking gap is used.

The crux of the peaking gap is the establishment of very high electric fields in the interelectrode

spacing. The velocity of propagation of the electron avalanche is proportional to the electric field

applied to electrodes, and thus, gap closure is dominated by the applied electric field. To produce

ultrafast switching, the spark gap is dramatically overvolted; that is, the spark gap is charged far in

excess of its self-breakdown voltage. Peaking gaps typically operate at gas pressures in the range of

100 atm and electric fields in the MV/cm range. The self breakdown curve for gases is known to

saturate in the vicinity of 100 MV/m for pressures to 50 atm. [3] To achieve overvolting without

switching at the self breakdown voltage, the spark gap is pulse charged very quickly. This allows a

large overvoltage to be achieved, and overvoltages of over 300% are achievable.

Interelectrode gap distance, 6, is chosen as small as possible to minimize the intrinsic inductance of

the spark channel, since the inductance is known to limit the achievable risetime of the resultant pulse.

Spark channel inductances of less than 1 nH have been achieved with gap lengths of 1 mm and less.

Because of the short gap lengths, even charge voltages of less than 100 kV can produce

interelectrode electric fields in the MV/cm range with voltage doubling at the spark gap. These small

interelectrode distances, however, yield high spark gap capacitances, even for relatively small

diameter electrodes. Moreover, this high spark gap capacitance, and the fast charging times lead to

1034

a strong displacement current which manifests as an undesirable prepulse on the load voltage. The

prepulse is observed on the output pulse with a magnitude, VW,

which is related to the capacitance

of the spark gap, C, by

(o’c

V&‘ Zoc—

dt

where ZOis the output impedance and Vc is the voltage which is applied to the spark gap. Since a

fast charge is critical to peaking gap operation, small diameter electrodes are desirable. Moreover,

minimizing the electrode diameter of the peaking gap may lead to enhanced periiormance. The

generation of 50 ps risetime pulse with a 60 kV charge in a single channel switch of very small

dimensions has been reported. [4]

PREDICTIVE RELATIONS

The spark gap is said to have closed when the potential difference between the electrodes is sharply

reduced and current becomes circuit limited. The predictions for the limitation of spark gap

technology are broken into two parts: the prebreakdown limitation and the post breakdown limitation.

The development of the prebreakdown phase of the spark development determines the minimum

closure time of the spark gap, which determines the risetime. Once the voltage across the channel has

collapsed, the electromagnetic wave must re-establish in the interradial distance. The post breakdown

phase consists of the inhibition of the voltage rise due to the inductance of the spark channel itself

Avalanche Propagation Limit

The breakdown of a spark gap initiates with an electron avalanche, even when a streamer mechanism

is operative. An avalanche initiates fi-om an initial electron distribution which maybe resident in the

gas, or from an external source. If the initial electrons are thermally distributed, the electron

population is small. The electrons accelerate under the influence of an external field. After some time,

the electron undergoes a collision with the background gas, with a resultant energy exchange. If this

energy exchange is sufficient, an ionizing collision occurs and an electron/ion pair is created. The

growth of the current density in this manner results in an electron avalanche. The growth of the

electron avalanche is described by the evolution of the electron number density. The electron number

density, N(t), grows from its initial value, NO, under the influence of an applied electric field,

according to

where v is the velocity of the electron, t is time, and a(v) is the electron ionization rate coefficient.

In general, the rate coefficient, U, is generally a finction of the relative velocity of the collision pair

and is gas specific. The above equation leads to the definition of the time constant related to the

1035

above equation, the avalanche growth time, given by

For gas pressures of 100 atm, avalanche transit times on the order of 1 ps has been calculated for

reduced electric field, E/p of 90 V/cm-torr. [5] If a single avalanche results in breakdown, the

associated risetime for avalanche growth is the risetime of the pulse. This treatment however assumes

the absence of the streamer mechanism and, thus, inherently assumes uniform field conditions apply.

It should be noted that this estimation is still valid when a streamer mechanism is operative. The

streamer mechanism initiates with an electron avalanche. The electron avalanche grows until the

electric field produced by the cumulative space charge in the avalanche head is on the order of the

applied field. The critical electron number for the avalanche to streamer transition is on the order of

10s. When this criteria is met, the discharge is said to have entered the streamer phase, The advent

of the streamer mechanism serves to greatly enhance the propagation speed of the discharge. Thus,

the major component of the discharge transit time is the electron avalanche development time.

Electromagnetic Propagation Limit

The electromagnetic propagation limit explores the timescale of the propagating wave in the

insulating mecha. Prior to breakdown, a spark gap is a capacitor. This capacitor, however, does not

necessarily charge filly before breakdown occurs. The spark gap cannot close in less time than the

transit time of the electromagnetic wave though the gap, as shown in Figure 2.

——

-!Ar i ‘O.

Figure 2.

The electric field lines as a pulse propagates through a spark gap prior

to breakdown. The field lines on the right hand side are the transmitted wave after

the spark gap switches.

To examine the propagation time in the spark gap spacing, the common scaling parameter Pb is used,

where P is the gas pressure, and 6 is the interelectrode gap distance. Thus, the transit time of an

1036

electromagnetic pulse through a spark gap filled with an insulating media with electric permittivity,

q and magnetic permeability, p, is

Ptr

Pa=—.

%

Thus for a high pressure gaseous spark gap, with an interelectrode gap spacing of 1 rmq the

minimum risetime is approximately 3 ps. However, for a spark gap inserted into a coaxial

transmission line, the risetime is determined not only by the gap closure but also by the re-

establishment of the propagating electric field in the inter-radial distance. The achievable risetime is

longer since the electromagnetic wave must be re-established between the inner and outer conductors.

Thus, the above limit must be modified by the interracial transit time, yielding,

where Ar is the difference between the outer and inner radii of the

transmission line. The resolution

time, then, for measurements is given by Ar (ep)x. For most high power systems, the inter-radial

distance, Ar, is made large to insure voltage holdoff in the coaxial systems. Of course, the breakdown

voltage is inversely proportional to both the inner radius and the logarithm of the radius ratio. Thus,

for ultrafast switching, for a given impedance, the inner conductor radius should be chosen to be

small.

Maximum Rate of Voltage Rise

Spark gaps are very good candidates for transferring high peak powers. However, the small radius

of the spark channel makes these switches intrinsically inductive and limits the achievable risetime by

inhibiting the rate of voltage rise, The spark gap is represented by the circuit of Figure 3, which is

valid once the discharge channel current is circuit limited. From this simple equivalent circuit, the

maximum rate of voltage rise, dV/dt, in the spark gap is calculated.

LS

Figure 3.

The equivalent circuit of the discharge channel

of a spark gap.

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When breakdown has progressed so that it is self sustaining, the single channel of the spark gap is

modeled as an inductor, L~. The coaxial transmission line feed of the equivalent circuit has an

inductance per unit length, L’, given by

L’ = ~ ln[~] ,

ri

where rOand ri are the outer and inner radii of the transmission line. The value of the inductance of

the spark channel, L~, can be difficult to calculate exactly. However, it has been shown that a very

good approximation can be obtained by treating the current carrying channel as a transmission line

of inner radius rCand outer radius rO.[6] Thus, the intrinsic inductance, ~, of the current carrying

breakdown channel is

where 6 is the interelectrode spacing of the spark gap. The inductance per unit length of the spark

gap, L~’, is

For a system with electrodes which are large compared to the channel radius, the value of the

inductance per unit length, L~’, of the spark channel can be approximated. For a system with large

electrodes, and reasonably low impedance,

r

o

— -30, 50, 100 .

r=

Since the natural logarithm fbnction is slowly varying,

ln[~] -4.

ri

Thus, the inductance of the spark channel can be approximated for practical purposes as

214J

L~’ -—

TG

The voltage across this equivalent inductor of the spark channel is given by

~=Lg

dt

The voltage rate of rise is expressed as

dV

=ZOG

z

dt

1038

where ZOis the feed impedance. Rearranging terms,

dv Zo ~

—= —.

dt L~

If the electrodes of the spark gap are large, and spaced a distance, 5, apart, the electric field is

uniform and given by

E=;.

The rate of voltage rise is related to the electric field by

dV ‘0 E

—=— ,

dt L~’

To estimate the maximum rate of voltage rise, let the electric field, E, be 100 MV/m, and the

impedance be 50 il. Thus, the maximum rate of voltage rise is

dV

—=

6“1015 ~ .

dt s

This estimate implies that for a switching voltage of 100 kV, the achievable risetime is on the order

of 10 ps. However, for a switching voltage of 1 MV, 100 ps is possible.

This estimate of the maximum rate of voltage rise in a spark gap is the order of magnitude which is

currently being produced through the use of peaking gaps. [1,4] The above equation suggests that the

even higher rates of voltage rise can be achieved by increasing the electric field on the spark gap and

reducing the inductance per unit length of the spark channel.

The Compensated Spark Gap: A Minimum Inductance Design

In ultrafast switching, the interelectrode spacing in the spark gap is chosen to be very short to

minimim the inductance of the spark channel. It can be showq in general, the inductance of the spark

channel in a spark gap dominates switch performance. This implies that by removing the additional

inductance caused by the reduced crossectional area of the spark channel in relation to the electrode

area, the switch characteristics will be completely determined by the inductance of the switch

hardware. For long gap spark channels this can be accomplished by the addition of a “taper” in the

outer conductor as shown in Figure 4.

The purpose of this taper is to match the impedance of the spark channel to the driving system

impedance and hence, matches the inductance per unit length of the hardware to the inductance per

unit length of the interelectrode gap region.

As shown in Figure 4, the sharp edges introduce

additional field enhancement to the spark gap design. A practical design contours both the inner

1039

conductor and the outer

throughout the switch.

conductor to maintain a constant impedance as well as the voltage holdoff

‘o

4

‘o —-zO——+

r,

~1

‘o

—

Figure 4.

The added dimension of the outer conductor compensates for the

reduced impedance of the spark channel radius.

This technique matches the

impedance of the spark channel to the driving system impedance. The taper dimension

is chosen so that the ratio rO/rCis equal to the ratio rO/r,.

Thus, fast single channel spark gap switching is optimized when the channel inductance per unit

length is that of the transmission line feed. Additionally, the system impedance is maintained

throughout the switch region, which eliminates the associated power loss. Thus, the notched spark

gap design provides the fastest risetime, while maintaining the system impedance mismatch.

CONCLUSIONS

The peak risetime which can be achieved has been examined in three ways: investigation of the critical

camier production rate to produce an electron avalanche which results in closure of a gaseous spark

gap; an examination of the limits imposed by the propagation of an electromagnetic wave in a

transmission line encased spark gap; the third method results from a circuit model of the spark gap

after breakdown. These calculations are in remarkably good agreement: risetimes on the order of

1-10 ps can be expected. Moreover, the calculations are independent, and thus, are not exclusive,

but complementary.

The above calculations provide guidelines for peaking switch design. Foremost, the electric field

which is applied to the switch is critical in determining the achievable risetime. The electromagnetic

wave calculations indicate the inner conductor dimensions should be minimized for a given

impedance. It has been shown that dtierent expectations are valid for achieving peak voltages of

different magnitudes.

Moreover, the notched spark gap design may alleviate the conclusions

regarding the maximum rate of rise.

1040

REFERENCES

[1]

[2]

[3]

[4]

[5]

[6]

W.D. Prather, C.E. Ba~ F.J. Agee, J.P. O’Laughlin, D.W. Schofield, J.W. Burger, J.Hull,

J. S.H. Schoenberg, and R. Copeland, “Ultrawide Band Sources and Antennas: Present

Technology, Limitations, Future Challenges,” Ultra Wideband/Short Pulse

Electromagnetic 3, Plenum Press, New York, 1996.

J.P. O’Laughlin and R.P. Copeland, “Subnanosecond Power Conditioning Technique Using

Transmission Line to Transmission Line Charging,” Proc, 20th Power Modulator Symposium,

pp. 351-354, 1992.

E.A. Avilov and N.V. Belkin, “Electrical Strength of Nhrogen and Hydrogen at High

Pressures,” Sov. Phys. Tech. Phys., Vol. 19, No. 12, June 1975.

C.A. Frost, T.H. Martin, P.E. Patterson, L.F. Rinehart, G.J. Rohwein, L.D. Roose,

J.F.Aurand, M. T.Buttram, “Ultrafast Gas Switching Experiments,” Proc. 9th IEEE Pulsed

Power Conference, K. Prestwich and W. Baker, Eds., pp. 491-494, 1993.

R.E. Cassell and F. Vill~’’High Speed Switching in Gases,” SLAC Publication 1858,

February, 1989.

S. hwinso~ E.E. Kunhardt and M. KristianseZ “Simulation of Inductive and Electromagnetic

Effects Associated with Single and Multichannel Triggered Spark Gaps,” Proc. 2nd IEEE

Pulsed Power Conilerence, A.H. Guenther and M. Kristiansen, Eds., pp. 433-436, 1979.

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