http://pps.coe.kumamoto-u.ac.jp/streaming/PulsedPower/generator/system1.htm1.4 Pulsed power generator system
1.4.1 Marx generator and water capacitor
A pulsed power system composing of a Marx generator and a water capacitor has been used for a long time, and is a mature technology. Fig. 1 shows a typical pulsed power generator. A high voltage produced by the Marx generator charges the water capacitor, which is composed of the coaxial electrodes and a water as a dielectric material. The energy of the water capacitor is transferred to the load through the main gap switch, the pulse transmission line, pre-pulse switch and MITL (.Magnetically insulated transmission line).
Fig. 1 Pulsed power system composing of a Marx generator and a water capacitor
The water capacitor works as a single line. After the main gap switch is automatically turned on by the high voltage charging of the water capacitor, the wave propagating to the Marx generator is reflected by its high impedance, and the wave propagating to the main gap switch is passing to the load satisfying the matching condition. As described in 2.3.1, a pulsed power with a pulse width 2l x er0.5/c and the voltage V0/2 is produced by the water capacitor, where er, l, V0 and c are the relative (specific) dielectric constant, the length and the charging voltage of the water capacitor, and the light velocity, respectively.
The voltage determined by the ratio of capacitances of the main spark gap switch and the transmission line is applied to the load during charging the water capacitor. This voltage is called the pre-pulse. In order to avoid the pre-pulse, the pre-pulse switch is placed. Since the load is frequently placed in the vacuum, the vacuum interface between the water and the vacuum is necessary. The MITL described in 3.2 transfers the pulse power to the load in vacuum.
(1) Marx generator
Fig. 2 Circuit of Marx generator
The Marx generator was invented by Marx , early in the twenty hundreds. Fig.2 shows the circuit of Marx generator. A DC high voltage power source charges capacitors to +V and -V for upper and lower sides of Fig. 2, respectively. The spark gaps and the triggered gap have potential differences of 2V and V, respectively. The triggered gap is turned on by a discharge caused by a high voltage pulse. The electric potential at "a" becomes zero (ground potential), and the potential of "b" becomes 2V. Since the potential at "c" is maintained to -V for a short time, considering a stray capacitance, the potential difference between 1 and 2 increases to 3V. Therefore, the spark gap turns on. Since the potential difference between 3 and 4 reaches to 5V, the spark gap shown with 3 and 4 turns on easily. The other spark gap turns on also, because of the potential difference of 7V between 5 and 6. The UV (Ultra Violet) light from spark gaps decreases a jitter of firing the spark gaps. Finally the voltage of nV is applied to load, where n is the number of capacitors.
Fig. 3 Trigger circuit of Marx generator
The Marx generator is placed in air or in oil. The Marx generator in air has a large inductance, since its size becomes large to keep the insulation by the air. Therefore the current risetime becomes large. To decrease the current risetime, the Marx generator is placed in oil. Fig. 3 shows the trigger circuit of spark gaps to decrease the jitter. The spark gaps of 1 to 3 are closed by triggered pulses. Since the voltage difference between the positive electrodes and triggered electrodes for the spark gaps of 4 to 6 reaches to 6V, these spark gaps are fired easily. In order to supply a large pulsed power to a load, the Marx generators in the oil, the water capacitors and the MITL are placed radially, starting from a load as shown in Fig. 4.
Fig. 4 Pulsed power system
(2) Energy transfer from the Marx generator to a water capacitor
Fig. 5 Energy transfer from Marx generator to water capacitor
The resistance of a pure water in a water capacitor can be neglected in a quick charging of a water capacitor within ms, since the impedance of the water capacitor is much smaller than the resistance. The schematic circuit of the energy transfer is shown in Fig, 5, where C1, C2 and L are the capacitances of the Marx bank and the water capacitor and the circuit inductance, respectively. The output voltage of the Marx bank is V0.
The voltage on C2 (Ref. Chapter1) is expressed as
(1)
At C1=C2,
(2)
At C1>>C2,
(3)
The energy transfer efficiency from C1 to C2 at t=p(LC)0.5 is expressed as
at C1=C2,
(%) (4)
at C1>>C2,
(%) (5)
The peak voltage on C2 and the energy transfer efficiency at C1=C2 are V0 and 100%, respectively. On the other hand, the peak voltage on C2 and the energy transfer efficiency at C1>>C2 are 2V0 and 4C2/C1x100 %, respectively. The water capacitor has been used as a pulse forming line (PFL) because of the large relative dielectric constant and the large dielectric strength. The oil and the solid dielectric material instead of the water have been used also.
1.4.2 Combination of transformer and PFL
A transformer charging the water capacitor or the oil capacitor as a PFL has been used instead of the Marx bank to produce a high voltage. Fig. 6 is a typical circuit of the pulsed power system using a transformer and a PFL. This system is compact and is able to be operated repetitively. The air core transformer immersed in the oil or the Freon gas is generally used for the wide range frequency characteristics and the high voltage insulation. The one turn primary coil is usual. After the capacitor C1 is charged, the triggered gap is fired. The energy in C1 is transferred to C2 of the PFL through the transformer. The pulsed power is applied to a load through the transmission line.
Fig. 6 Pulsed power generator using transformer and PFL
Fig. 7 Equivalent circuit of Fig. 6.
The energy transfer from a capacitor to another capacitor through a transformer has been known from an analysis of the Tesla coil. The self inductances of the primary and the secondary windings are L1 ad L2, and the mutual inductance is M.. The coupling coefficient K is expressed as
(6)
The conditions for a maximum energy transfer of about 100% are
(7)
(
from an analysis of the Tesla coil. In order to satisfy the two conditions of Eqs. 7 and 8, a tuning inductance L20 in Fig. 6 is inserted. The conditions to get a maximum energy transfer are
(9)
(10)
Two values of L20 at K=0.6 are obtained from Eqs. 9 and 10. The energy transfer of about 80 % is obtained by selecting a value between two values.
1.4.3 Inductive energy storage and opening switch
Fig. 8 Pulsed power generator using inductive energy storage system
A compact and light weight pulsed power generator is constructed by using an inductive energy storage and opening switches. Fig. 8 shows a typical pulsed power generator. The capacitor C is charged, and then discharged through the inductor and exploding wires (fuses) by triggering the spark gap. The resistance of exploding wires increases with increasing energy input, changing the states such as the solid, the liquid and the vapor. The exploding wires are operated as an opening switch by the increase of the resistance. Fig. 9 shows typical waveforms of current through, voltage across and resistance of exploding wires. The circuit upper than the exploding wires is disconnected. The current decreases and the voltage increases quickly with the increase of the resistance of exploding wires. An induced voltage of LdI1/dt corresponds to the voltage drop on exploding wires, R(t)xI1, since the voltage on the capacitor is zero after the energy transfer from the capacitor to the inductor.
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Fig. 9 Typical waveforms of current through, voltage across and resistance of exploding wires
The current flows into a plasma of a plasma opening switch after the exploding wire turns off the high current, and then the plasma opening switch turns off the current. The current flowing through the plasma is transferred to the load. Fig. 10 shows the current waveforms of I1, I2 and I3 in Fig. 8 for a short circuit load. The current risetime of I3 is much shorter than that of I1. Since the conduction time of the plasma opening switch is short (less than 1ms), the exploding wire is used to get an enough time of the energy transfer from the capacitor to the inductor. The performance of this pulsed power system strongly depends on the characteristics of the opening switch.
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Fig. 10 Current waveforms for a short circuit load
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1.4.4 Magnetic pulse compression
A pulsed power system using a magnetic pulse compression (MPC) circuit can be operated at a high repetition frequency of about 1000 Hz. Therefore, this system has been used for industrial applications, especially pulsed lasers.
(1) Magnetic pulse compression circuit
The concept of MPC circuit is explained by using Fig. 11. After the C1 is charged to V0, the switch is turned on. The energy in C1 is transferred to C2. During the energy transfer from C1 to C2, the saturable inductor L2 keeps an unsaturable state. Therefore only a small current flows through L2 and C3, since the inductance of L2 is much larger than L1. Just after the energy transfer from C1 to C2, the saturable inductor saturates. A capacitor C2 discharges through L2 and C3, since the inductance of the saturated inductor is much smaller than L1.
Fig. 11 Concept of MPC circuit
The inductances of the saturated and the unsaturated inductors are expressed by L2s and L2u, respectively. The conditions of C=C1=C2=C3 and L2s<<L1<<L2u are assumed. During the energy transfer from C1 to C2, the peak current I1max and the voltage on C2, V2(t) are
(11)
(12)
where and .
The inductance of L2 changes from L2u to L2s at the time of t=p(L1C0)1/2, when the energy transfer from C1 to C2 finishes. Since L1>>L2s, the energy in C2 is transferred to not C1 but C3. The current amplification factor is
(13)
The pulse width is 1/hc times. The peak voltage is the same amplitude.
(2) Saturable inductor
A saturable inductor changes from an unsaturated state to a saturated state, and its inductance decreases quickly. Therefore the saturable inductor can be used as a closing switch. The inductance of a straight solenoid coil is,
under the unsaturated state,
(14)
under the saturated state,
(15)
where A, N and l and are the cross section, the turns' number and the length of the solenoid coil, respectively. mru and mrs are the relative (specific) magnetic permeability of a core under the unsaturated and the saturated sates, respectively.
From ,
(16)
where Bs and Ts are the saturation magnetic flux density and the time from the unsaturated to the saturated state, respectively. From Eqs. (12) and (16),
(17)
In order to keep the unsaturated state of the core till t=p(L1C0)1/2 (=Ts) , a ferromagnetic material with the cross section, A, is necessary. A roll of a thin amorphous metal and a thin kapton film are used as the saturable inductor. Fig. 12 shows an example of the saturable core placed into the strip line.
Fig. 12 Saturable inductor
(3) Multi-staged magnetic pulse compression circuit
The examples of multi-staged magnetic pulse compression circuits are shown in Fig. 13 (a) and (b). Just after the energy of a capacitor is transferred to the another capacitor, the inductor of the next stage is saturated. Then the energy is transferred by and by.
(a)
(b)
Fig. 13 Multi-staged magnetic pulse compression circuits
The circuit (a) is composed of the capacitors with the same capacitance, the inductors with a different saturated inductance, the switch and a load. The peak voltage on each capacitor is the same. The pulse widths t1 to t3 change for the currents I1 to I3. The compression ratio of the pulse width is
(18)
The efficiency of the energy transfer is 100%.
The circuit of Fig. 13 (b) has the capacitors with a different capacitance and the inductors with the same saturated inductance. The peak voltage on C is higher than that on 1000C. The voltage amplification ratio is calculated as
(19)
where V1 and V3 show the voltages on 1000C and C, respectively. The voltage on C is amplified to 6 times of the voltage on 1000C The pulse width is compressed as
(20)
The efficiency of the energy transfer from 1000C to C is easily calculated as
(21)
where E1 and E2 are the maximum stores energy in 1000C and C, respectively. The efficiency of the energy transfer is only 3.6%
1.4.5 Inductive voltage adder
The principle of a linear induction accelerator is applied to a system of pulsed power generator, which is called the inductive voltage adder.
(1) Principle of a linear induction accelerator
Figs. 14 and 15 show the schematic diagrams of the electrostatic and the linear induction accelerators. The electron beam is extracted from the beam source and accelerated by the electric field. The beam source is the high voltage with a negative polarity in the case of the electrostatic accelerator The toroidal ferromagnetic material is used in the case of the linear accelerator to achieve a multi-staged connection. A small current i' flows around the ferromagnetic material, and a large current iB which is almost the same amplitude with the source current i flows through the beam. The high voltage is not observed if the voltmeter is connected like in Fig. 15, since the flux change does not occur. However, a high voltage is observed if the voltmeter is connected inside the accelerator, since the flux change occurs.
Fig. 14 Electrostatic accelerator
Fig. 15 Linear induction accelerator
Fig. 16 shows a typical circuit of a linear induction accelerator, which has a multi-staged connection. The multi-connection of the electrostatic accelerator is impossible.
Fig. 16 Principle of the linear induction accelerator
(2) Inductive voltage adder
Fig. 17 shows the system of a pulsed power generator, which uses the principle of the linear induction accelerator. The solid electrode placed in vacuum is used instead of the beam. The vacuum keeps the insulation. The characteristic impedance along the line increases gradually by changing the diameter of the inner electrode in order to satisfy a matching condition. The voltage at load becomes nV0, where n and V0 are the number of the ferromagnetic core (cavity) and the voltage applied to the cavity, respectively
Fig. 17 Pulsed power generator using the principle of the linear induction accelerator.
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The saturation of the ferromagnetic material causes the increase of the current around it, and the system does not work as the inductive voltage adder. Therefore, the cross section of the material must be large, satisfying the following equation,
(22)
where t is a pulse width of V0.
1.4.6 Explosive generator
The chemical energy of an explosive transforms to a kinetic energy or an electromagnetic energy, and then the pulsed power is obtained. The advantage of a pulsed power system using the explosive is an extremely high energy density and very compact. The disadvantage is a single shot operation.
Fig, 18 shows a typical explosive generator. After the switch S is turned on, the energy in capacitor is transferred to that in the inductor with the circuit. Then the exploder is operated, and the area of the circuit decreases by the explosive as shown in the lower figure of Fig. 18. The current increases with the decrease of the circuit inductance, since the magnetic flux, namely the current multiplied by the inductance, is constant. The current after the initiation of the explosive, I, is expressed as
(23)
where L0 and L are the circuit inductance before and after the initiation, respectively. I0 is the initial current. The ration of the inductively stored energy after the initiation on that before the initiation is
(24)
The stored energy after the initiation increases L0/L times of that before the initiation. Fig. 19 shows the explosive generators of spiral and coaxial configurations, respectively. In the case of the spiral configuration, the current and the energy amplification ratios are large, but the risetime is long. In the case of the coaxial configuration, the risetime is short, but the amplification factor is moderate. A pulse transformer is used for a load which needs a high voltage.
Fig. 18 Typical explosive generator
Fig. 19 explosive generators of spiral and coaxial configurations
1.4.7 LC generator
Fig. 20 shows the LC generator, which is used instead of the Marx bank. The capacitors are charged, and the direction of the electric field is shown by arrows of the left hand side. The output voltage is zero. After the switches are turned on at the same time, the LC oscillation occurs through the switch, the inductor and the capacitor. The direction of the electric field reverses at t=p(LC)1/2 . Then the electric field looks towards the same direction as shown by arrows of the right hand side. The output voltage is nV, where n and V are the number of capacitors and the charging voltage of each capacitor. Though the circuit is simple, it is difficult to turn on the switches at the same time. The 100% voltage reversal of capacitor is a problem too.
Fig. 20 LC generator
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