Multiconcentric coaxial cable pulse forming device

A multiconcentric coaxial cable uses three or more concentric cables to supply power to a high voltage laser with reduced waveform degradation otherwise produced by stray capacitance and inductance. Each pair of concentric conductors is in itself a coaxial line and the radius of each conductor is selected such that the characteristic impedances of the two lines it forms with the adjacent conductors are equal. Each line is charged with a polarity opposite to the adjacent lines. Polarity inverting switches are connected across the lines charged to the polarity opposite to the desired output polarity at the end of the cable opposite from the load connection. The load is connected to the outermost cable conductor of the cable. When the switches are closed the polarity of the cable sections to which they are connected reverse and the sum of the voltages on all the cable sections is applied to the self-breaking gap causing it to close and connect the load. The sum of the impedances of the cable sections is designed to be equal to the load impedance and therefore the energy from the cable to the load is matched.

BACKGROUND OF THE INVENTION 
The present invention relates generally to lasers requiring high voltages, 
and more specifically to pulse forming networks which are formed from 
coaxial cables. Coaxial cables have been used as pulse forming networks 
(PFN) since before 1940, and were the basis for the derivation of the 
canonical lumped parameter networks during WW II. The pulse fidelity from 
cables is unequaled but there are some limitations and disadvantages 
inherent with their use. The most significant limitation is the length of 
cable required, typically about 90 meters per microsecond. Another 
limitation is the practical range of characteristic impedance being about 
10 to 100 ohms, but this at least is within the range of many PFN 
applications. Both of these limitations are somewhat overcome by the 
lumped parameter PFN, usually with an acceptable degradation in pulse 
fidelity. However, when scaling to very high voltage and energy, problems 
arise with the lumped parameter PFN which begin to put them at a 
disadvantage with respect to coaxial lines. Specifically, stray inductance 
and capacitance of the lumped parameter PFN causes serious degradation of 
pulse fidelity. A coaxial cable is a distributed parameter device and the 
stray problems with scaling does not exist. Another disadvantage with 
conventional cable PFN systems is the size and volume required. When 
lumped parameter devices such as conventional PFN's, Blumlein's Marx 
generators, etc., are scaled up, they require large oil filled tanks which 
are also very costly. The actual cables themselves are self contained 
regardless of the size, and can be orders of magnitude smaller in the 
overall space required and the total cost. 
The task of providing a pulse forming device using coaxial cable technology 
without high space requirements, and without waveform degradation due to 
stray capacitance and inductance is alleviated, to some degree, by the 
following U.S. Patents, the disclosures of which are incorporated by 
reference: 
U.S. Pat. No. 3,463,992 issued to Solberg; 
U.S. Pat. No. 3,845,322 issued to Aslin; 
U.S. Pat. No. 4,005,314 issued to Zinn; 
U.S. Pat. No. 4,484,085 issued to Fallier, Jr. et al; and 
U.S. Pat. No. 4,549,091 issued to Fahlen et al. 
Zinn discloses a device for achieving a narrow high voltage output pulse 
having a rise time essentially limited only by the rise time of the 
switching means. It comprises a voltage source connected through a 
semiconductor switch to an energy storage device. This device uses a 
plurality of capacitors fabricated similarly to a conventional coaxial 
cable, but includes a plurality of conductive elements with insulating 
means disposed between each element. Holdoff semiconductor diodes are 
connected to the coaxial elements and a load is connected between the 
outer element and ground. The capacitors of the reference are charged in 
parallel from the single power source and discharged in series through a 
second current path which includes the common load. 
Soldberg discloses a capacitive storage system which employs capacitors 
having different time constants and charged with a voltage magnitude and 
polarity different for each capacitor. This patent discloses two 
capacitors in series charged separately to unequal voltages of opposite 
polarity for long term energy storage. 
Aslin shows a Marx type pulse generator. Fahlen et al discuss a pulsed 
electrical power circuit for high repetition rate gas lasers. In Fallier, 
Jr. et al a pulse generator is formed by overlapping conductive spiral 
strips separated by insulating strips. 
Pulse forming networks composed of coaxial cables which use two conductors 
provide comparatively low energy storage utilization, have high cost and 
space requirements and produce waveform degradation due to stray 
capacitance and inductance. There remains a need in the art to provide a 
pulse forming device which reduces these problems. The present invention 
is intended to satisfy that need. 
SUMMARY OF THE INVENTION 
The present invention provides a pulse forming device for lasers which 
require high voltage using a multiconcentric coaxial cable, and a 
plurality of polarity inverting switches. The multiconcentric coaxial 
cable uses three or more concentric waveforms to obtain pulse waveforms as 
described below. 
Note that each pair of concentric conductors, in the multiconcentric cable, 
act as a coaxial line. The radius of each conductor is selected to match 
its impedance with adjacent conductors. 
Each conductor is charged with a polarity which is opposite that of 
adjacent conductors. The polarity inverting switches are connected across 
the conductors, and charged to the polarity which is opposite to the 
desired polarity at the end of the cable opposite from the load. 
The load is connected to the outermost cable conductor, and through a 
self-breaking gap to the centermost conductor. When the switches are 
closed the polarity of the cable sections to which they are connected 
reverse and the sum of the voltage on all the cable sections is applied to 
the self-breaking gap causing it to close and connect the load. The sum of 
the impedances of the cable sections is designed to be equal to the load 
impedance and therefore the energy transfer from the cable to the load is 
matched. 
It is an object of the present invention to provide a pulse forming device 
that solves the problem of low energy storage utilization which usually is 
inherent in two conductor cable systems. 
It is another object of the present invention to provide a pulse forming 
device that reduces laser waveform degradation caused by stray capacitance 
and inductance. 
It is another object of the present invention to reduce the cost and space 
requirements of high voltage pulse generators.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
The present invention is a multiconcentric coaxial cable pulse forming 
device. 
The reader's attention is now directed towards FIG. 1 which is a schematic 
of an end view of a coaxial cable. Some of the major items involved with 
cable technology are the design of the termination and the utilization of 
dielectric material in capacitors vs. cables. The energy storage per unit 
volume (specific energy) in a conventional capacitor is uniform and much 
higher than that in a coaxial cable. This is due to the fact that the 
maximum allowed electric field (E) in a cable dielectric is limited to the 
area adjacent to the inner conductor and falls off inversely with the 
radius. Since the specific energy is proportional to the square of E the 
utilization of the total dielectric in a cable is poor. In a capacitor all 
the dielectric is stressed at the maximum E and the utilization is 
optimum. 
The relevant equations for a coaxial cable, as depicted in FIG. 1, are: 
##EQU1## 
where: Zo=characteristic impedance; 
Em=maximum electric field (at the inner conductor surface); 
.epsilon.=relative permitivity of the dielectric; 
d1=inner diameter; 
d2=outer diameter; 
E(r)=electric field at radius r; and 
V=the voltage between the conductors at d1 and d2. 
FIG. 2 is a schematic of an end view of the multiconcentric cable used in 
the pulse forming device of the present invention. A multiconcentric 
coaxial cable simply has more than two concentric conductors as shown in 
FIG. 2. The equations (1), (2) and (3) can be applied to the system of 
FIG. 2, with the appropriate bookkeeping. The numbering will always be 
taken from the inner conductor outward. That is, as Equation 1 presented a 
single impedance Zo for a coaxial cable, the equations for the impedance 
of a triaxial cable are as in equations presented below: 
##EQU2## 
where .epsilon. equals the dielectric permitivity. 
FIG. 3 is a schematic of a Blumlein circuit using the triaxial cable of 
FIG. 2. The inner and outer sections have the same characteristic 
impedance and are charged to opposite and equal voltage. The load Zo is 
connected between the inner conductor and a shorting switch (x) is 
connected across one of the sections at the opposite end of the line. When 
the switch x closes the voltage reverses and the two sections of line 
discharge into the load. In FIG. 3, an arrangement analogous to a Marx 
generator/Blumlein combination is applied to a multiconcentric cable. The 
advantage is that the full voltage is only obtained at the time of 
discharge, and the energy is stored at a voltage reduced in corresponding 
to the number of concentric sections. 
Analysis of the energy utilization shows that in FIG. 3, there is no 
improvement over the case of the same cable (i.e., the same o.d. and i.d.) 
configured as a simple two conductor coax and charged to the same total 
erected voltage. In fact, the utilization is slightly degraded in the 
multiconcentric due to the additional thickness of the extra conductors. 
Now consider the same multiconcentric cable with equal characteristic 
impedances but with a different charging voltage applied to each section 
so that the field gradient E at the surface of the inner conductor of each 
section is at the maximum rated value. Now the outer sections will be 
charged to higher voltages because of the larger radii and the utilization 
of the dielectric is improved. There is no problem with the voltage 
division when the switches erect because all the sections are the same 
impedance even though they are charged to different voltages. There is one 
problem in that the sum of the voltages no longer equals zero, so the 
inner conductor cannot be connected to the load during the charging 
period. This is easily fixed by adding a self-breaking gap as shown in 
FIG. 4. The magnitude of this voltage "unbalance" is held to a minimum if 
an even number (N) of sections are used. 
FIG. 4 is a schematic of the multiconcentric coaxial cable pulse forming 
device of the present invention. This pulse forming device supports a load 
400 of impedance Zo. This load 400 is electrically connected by a hold-off 
gap 401 to the center conductor 403 of the multiconcentric coaxial cable, 
and to a common electrical ground shared by the outermost conductor 404 of 
the cable. The multiconcentric coaxial cable thereby supples high voltage 
to the load from two voltage sources V(1) and V(2) in accordance with the 
equations below: 
##EQU3## 
Note that the present invention is not limited to the triaxial system of 
FIG. 4. 
Consider an N section Multiconcentric cable which is to have a matched 
erected impedance of Zo with each section operating at the maximum stress 
Em. Then for each section: 
##EQU4## 
and this fixes 
##EQU5## 
for all n, The outer diameters are related to the inner diameter d(1) as: 
##EQU6## 
The voltage between the n and n+1 conductor is designated as V(n) and is 
given by: 
##EQU7## 
The term .sqroot..epsilon. *Zo occurs frequently and is defined as; 
##EQU8## 
Using (12) and (13) the total erected voltage Vp can be expressed as: 
##EQU9## 
and the total outside diameter d(N) is given by: 
##EQU10## 
The dielectric utilization for energy storage can be calculated by 
integrating the energy storage over the multiconcentric cable and dividing 
by the energy that would be stored if the dielectric were under constant 
maximum stress. The energy storage rating factor J% is given as: 
EQU J%=Q((30*N)*(EXP (Q/(30*N))-1) (17) 
The voltage grading ratio's required to maintain the peak stress on the 
inner diameter of each of the N sections of a multiconcentric is given by: 
##EQU11## 
Where V(N,j) is the voltage between the j and j+1 conductors of an N 
section cable. 
The residual voltage, i.e., the voltage which the load isolation gap must 
hold off, is held to a minimum by using an even number (N) of sections and 
is calculated by summing equation (18) with alternate signs for each term. 
The outside diameter of a cable can be evaluated as a function of Q and N 
by writing equation (14) as; 
##EQU12## 
Equation (19) shows that there is clearly an optimum Q for a minimum 
diameter and that the diameter does decrease for increasing N. 
Much more impressive is the comparison of energy stored per unit volume of 
cable. The volume is taken to be a full cylinder of the outside diameter. 
The expression giving the specific energy Js is; 
##EQU13## 
Where: c=3E8 meters/sec (speed of light) 
Js=energy density joules/cubic meter 
Em=maximum gradient volts/meter 
Equation (20) shows a very significant improvement in specific energy for 
increasing N as well as optimum values as a function of Q. 
The difference in specific energy at optimum Q, between a single 
conventional cable and a two section (triaxial) is about six times in 
favor of the triaxial. A four section is about 25 times better and a six 
section 60 times better in terms of energy stored per unit volume of 
cable. These improvements are translated to reductions in volume, weight 
and cost when they are applied to the same load. 
FIG. 5 is a specific embodiment of the present invention which uses a 
multiconcentric cable 500 to supply a load of 10 ohms with power from four 
voltage supplies 501-504 according to the design principles described 
above. The system of FIG. 5 is required to drive a 10 ohm load with a 2.5 
microsecond pulse at 2 MV. The peak erected voltage Vp is 4 MV for a 
matched output of 2 MV. The design of FIG. 5 uses conservative values of 
2000 volts/mil (78.74 MV/meter) and an .epsilon. of 2.7. The optimum Q 
with N=4 is 50, which gives a Zo of 30 ohms. So three parallel cables will 
be used to drive the 10 ohm load. With N=4, the diameter of the cable is 
found to be 0.2023 meters or 8 inches. The voltages of the four sections 
are found to be 0.178, 0.129, 0.270, and 0.333 normalized to the peak 
charge voltage of 4 MV. The length of the cable for a 2.5 microsecond 
pulse and .epsilon. of 2.7 is 228 meters (749 feet). The volume of the 
three cables is 22 cubic meters or 776 cubic feet and would weigh about 
43,738 Kg (96,225 lbs.). The stored energy is 1 MJ or about 10 joules per 
pound which is less than the specific energy of conventional capacitors, 
but that is not the whole story. Using a lumped parameter store of 
capacitors requires a huge tank of oil which adds up to much more total 
weight and volume than the cable. In addition, the cable waveform, in the 
system of FIG. 5, is not deteriorated by the stray inductance and the 
cable is nowhere near as mechanically awkward. The cable is only eight 
inches in diameter and plugs into the load with only a hold-off gap. The 
cable is so small that the space near the load is not cramped. The switch 
assembly is at the far end of the cable and can be located in a convenient 
place. The cable is flexible and can be coiled or laid in a trench or 
overhead rack. Furthermore, if a stress of 3000 volts/mil is used the size 
drops to only 5.4 inches diameter and the volume and weight become 9.8 
cubic meters (345 cubic feet) and 19,440 Kg (42,767 lbs.). 
The design and method of attaching the switches to multiconcentric cables 
is an important consideration. A conceptual design using concentric gap 
switches is shown in FIG. 6. As depicted in FIG. 6, the four conductor 
multiconcentric cable 600 is equipped with four concentric mid-plane gas 
switches 601-604 which each bridge adjacent conductors through voltage 
graded insulation surfaces in the cable. As described above, this system 
reduces the cost and space requirements of high voltage pulse generators 
and solves the problem of waveform degradation due to stray capacitance 
and inductance. 
While the invention has been described in its presently preferred 
embodiment it is understood that the words which have been used are words 
of description rather than words of limitation and that changes within the 
purview of the appended claims may be made without departing from the 
scope and spirit of the invention in its broader aspects.