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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.
1033
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.
1037
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
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C.A. Frost, T.H. Martin, P.E. Patterson, L.F. Rinehart, G.J. Rohwein, L.D. Roose,
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Power Conference, K. Prestwich and W. Baker, Eds., pp. 491-494, 1993.
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February, 1989.
S. hwinso~ E.E. Kunhardt and M. KristianseZ “Simulation of Inductive and Electromagnetic
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