Repetitively Pulsed High-Current Accelerators with Transformer Charging of Forming Lines

Repetitively pulsed high-current accelerators with transformer charging of forming lines

GENNADY A. MESYATS, SERGEI D. KOROVIN, ALEXANDER V. GUNIN, VLADIMIR P. GUBANOV, ALEKSEI S. STEPCHENKO, DMITRY M. GRISHIN, VLADIMIR F. LANDL, and PAVEL I. ALEKSEENKO Institute of High-Current Electronics, Siberian Division, Russian Academy of Sciences, Tomsk, Russia ~Received 1 April 2003; Accepted 16 May 2003!

Abstract This article describes the principles of operation and the parameters of the SINUS setups designed at the Institute of High-Current Electronics, Siberian Division, Russian Academy of Science, over the period from 1990 to 2002. A characteristic feature of accelerators of the SINUS type is the use of coaxial forming lines ~in particular, with a spiral central conductor! which are charged by a built-in Tesla transformer to produce the accelerating high-voltage pulses. This ensures a reasonable compactness and long lifetime of the setups. The range of parameters of the SINUS setups is as follows: • Voltage amplitude at the cathode: 200–2000 kV • Electron beam current: 2–20 kA • Equivalent load impedance: 30–180 V • Accelerating pulse duration: 4–130 ns • Pulse repetition rate: up to 400 Hz • Pulse amplitude instability ~RMS!: 0.7–2.5% A number of setups of this type use a three-electrode controllable gas gap switch. This has made possible on-line electronic control ~from pulse to pulse! of the output voltage pulse amplitude. The control band width d ϭ DU0Umax was up to 75%. Studies have been performed on the lifetime of explosive-emission cathodes. At current densities of 25–30 A0cm2, a pulse duration of ;20 ns, and a pulse repetition rate of 100 Hz, the metal-dielectric cathode in a planar geometry retained its emissivity within 108 pulses. The SINUS accelerators are traditionally employed for producing high-power microwave radiation in various systems with a coaxial electron beam in a longitudinal magnetic field. For this purpose, magnetic systems with a solenoid powered from the bank of molecular capacitors have been designed. The duration of a quasistationary magnetic field was1satamaximum solenoid power of 365 kW. The possibility has been shown to exist for a self-contained power supply of the accelerator from the bank of molecular capacitors in the batch mode. With an average power consumption of about 120 kW, the setup produces pulses in a batch of duration 2.5 s at a pulse repetition rate of 200 Hz. Keywords: Molecular capacitor; Pulse forming line; Tesla transformer; Trigatron; Vacuum diode

1. PRINCIPLES OF THE DESIGN In each module, time energy compression occurs, result- OF THE SINUS SETUPS ing in an increase in transferred power. The characteristic times of the processes at each step are: seconds— The main idea used as the basis for the operation of the milliseconds—microseconds—nanoseconds. The energy SINUS accelerators is relatively slow energy storage from a conversion takes place on sequential operation of controlla- power supply with its subsequent fast utilization. Figure 1 ble switches. In the primary low-voltage circuit these are shows the block diagram of consecutive energy conversion thyristor switches; in the secondary high-voltage circuit it is in the SINUS setups. a gas gap switch. The energy is transferred from the capacitive store Tesla Primary to Forming Line through a step-up Address correspondence and reprint requests to: Alexander V. Gunin, High Current Electronics Institute SD RAS, 4AkademicheskyAve., 634055 transformer in the mode of free oscillations. The open mag- Tomsk, Russia. E-mail: [email protected] netic core provides a high coupling coefficient between the 197

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cuits. The following relation determines the optimum value of the coupling coefficient k:

2N k ϭ k ϭ , opt N 2 ϩ 1

Fig. 1. Energy conversion in a SINUS accelerator. here N is an odd number integer. Particularly, for N ϭ1, 3, 5 we have kopt ϭ 1, 0.6, 0.385. The value ~N Ϫ 1!02 specifies the number of changes in the sign of the charging voltage of transformer circuits. Matching of self-oscillation frequen- the energy store within the time the store is charged. With cies of the transformer circuits allows highly efficient en- d ϭ ~1Ϫ k! ϽϽ 1, the capacitive energy store can be charged ergy transfer. Forming Line is a long coaxial pulse forming without a change in the sign of the charging voltage. line. The geometrical sizes of the line determine its electri- To increase the electric strength of the forming line and cal length and wave impedance. Upon the operation of the also to provide the possibility of employing a thyristor switch gas gap switch, a voltage-dump wave is generated in the line in the primary circuit of the Tesla transformer, the coupling and a nearly rectangular voltage pulse is formed across the coefficient between the circuits in the high-voltage genera- load. The forced circulation of the gas in the discharge gap tors designed was chosen to be close to unity. The geometry and trigatron control of the breakdown makes it possible to of this system is presented in Figure 3. produce accelerating pulses with a high repetition rate and The open ferromagnetic core built in the forming line is with an amplitude stability of no worse than 1–3%. When employed for increasing the coupling coefficient. In this operated in the batch mode, the setup employs an additional case, the coupling coefficient depends only slightly ~com- energy store composed of molecular capacitors. The elec- pared to a closed core! on the properties of the ferromag- tronic system of voltage stabilization in the primary store netic core material, being completely determined by its makes it possible to use up to 50% of the energy stored in the geometrical parameters. In particular, for the case where the molecular bank. This ensures an independent power supply length of the magnetic core is much larger than its external of the accelerator with a power consumption of hundreds of radius, kilowatts within a pulse batch of several seconds duration. 2 8 r2 k 2 Ϸ 1 Ϫ F~b!ͩ ͪ, 3 l 2. TESLA TRANSFORMER M Theoretical consideration of the operation of a Tesla trans- where F~b!ϭ$a@~ b Ϫ1!~2bϩ1!# 0b 2 % ln~b!;bϭr 0r ;r , former combined with a forming line of the accelerator was 2 1 2 r1 are the radii of the inner and outer conductors of the given by Eltchaninov et al. ~1981, 1983!. The electric circuit forming line; lM is the magnetic core length; and a is a of the generator based on the use of a Tesla transformer is coefficient dependent on the geometry of the secondary coil presented in Figure 2. of the Tesla transformer ~a ; 1!. It follows from this figure that the Tesla transformer is a The achievable value of the coupling coefficient in these system of two inductively coupled circuits operating in the systems is k ; 0.85–0.95. So, this allows a rather high mode of free oscillations. The system allows converting of efficiency of charging of the accelerator forming line during constant or quasiconstant voltage to high-voltage pulsed the first half-wave of the charging voltage. The efficiency of voltage. The maximum efficiency of energy conversion ~from charging without detuning of the self-oscillation frequen- C1 to CFL! in the Tesla transformer is attained at properly specified values of the coupling coefficient between its cir-

Fig. 3. Coaxial geometry of the Tesla transformer built in the forming line. 1: outer and inner conductors of the coaxial forming line, 2: external and Fig. 2. Simplified electric circuit of a high-voltage generator based on the central paths of the open ferromagnetic core, 3: primary winding of the use of Tesla transformer. Tesla transformer, 4: secondary winding of the Tesla transformer.

cies of the Tesla transformer circuit is determined by the cuit, there are actual inductance of the primary circuit LC , expression resistance of elements of the primary circuit R1, and resistance of the secondary circuit R2. The circuit is reduced to E p 2 the primary circuit by using the effective transformation ϭ 2 Ϸ Ϫ Ϫ 2 h 1 ~1 k !, Ϸ 0 Ϸ 0 0 E1 8 coefficient ns N2 N1 !Lsec L1, where N2 N1 is the ratio of the number of turns in the transformer secondary and

where E2 is the energy stored in the forming line, and E1 is primary. The values for the quantities present in the equiv- the energy stored in the Tesla transformer primary. Nor- alent circuit satisfy the following relations ~compare Figs. 2 mally, h.0.8, if ~r2 0lFL!,0.25. In the case of detuning and 4!: between the circuits, part of the stored energy remains in the ϭ ϩ ϩ ϭ 2 primary store and can be used in the next cycles of charging L1 Lm Ls1 LC R2 Rsec ns of the forming line. ϭ 2 ϩ 2 ϭ 0 2 The time it takes for the forming line to be charged is Lsec ns ~Lm Ls2 ![ns L2 C2 CFL ns determined by the time an electromagnetic wave takes to ϭ ϭ propagate through the windings of the secondary coil of the M ns Lm I2 Isec{ns, Tesla transformer. Allowing for nonuniformity of the elec- where L and L are the leakage inductances in the primary tric field distribution in the coaxial line, this time is equal to s1 s2 and secondary circuits of the Tesla transformer and Lm is its M magnetizing inductance. The current in the two loops of the « 102 tch Ϸ 2p{r2 N2 @F~b!0ln~b!# , equivalent circuit are described by the following system of c equations:

where N2 is the number of turns of the secondary coil and 1 ! '' ϩ ' ϩ ϭ '' c0 « is the light speed in a dielectric of permittivity «. L1 I1 R1 I1 I1 Lm I C1 The value of the operating voltage of the primary capac- ~1! Ά '' ' 1 '' itive energy store is not higher than 400–700 V, which al- ϩ ϩ ϭ L2 I2 R2 I2 I2 Lm I1 . lows employing thyristor switches as the primary switch of C2 the Tesla transformer. The charging voltage of the forming line is specified by the relation between the number of turns At the instant the switch S operates, we have the following ϭ ϭ ϭ ϭ in the secondary and primary windings and by detuning of initial conditions: UC1 U0, UC2 0, I1 I2 0, where UC1 the circuits. and UC2 are the voltages across the capacitors C1 and C2 at It is possible to use the above method for charging the the initial moment in time. Numerical integration of system forming line only if the coupling coefficient between the ~1! by the Runge–Kutta method makes it possible to calcu- circuits of the Tesla transformer is high. This requirement late the current and the voltages with a percentage error of imposes a limit on the choice of the forming line geometry. no worse than 0.001% for a wide range of values of the circuit elements ~Fig. 4!. Typical waveforms of the current Particularly, the condition lFL ϾϾ r2 should be fulfilled. With a specified value of the charging voltage this condition set and voltage in the circuits of the Tesla transformer are shown the lower limit on the line length and, consequently, on the in Figure 5.At some moment in time tx, ~a! the breakdown of ϭ ϭ duration of the pulses formed due to the limited electric the gas gap switch ~tx Tbreak, UC2 Ubreak! and ~b! the strength of the forming line. It should be noted that this closing of the thyristor switch S when the current I1 changes ϭ ϭ limitation corresponds to the requirement of the absence of its direction ~tx Topen, I1 0! occurs. These points are simulated by varying C2 and LC and by resetting the condi- high-order modes within the time a pulse is formed in the ' ' coaxial line. tions for UC2~tx !, I1~tx !, I1~tx !, and I2~tx !. With high coupling coefficients, it is convenient to present The discrepancy between the calculated values and the the system of two inductively coupled circuits ~Fig. 2! as the values measured in the actual setups is not higher than sev- circuit shown in Figure 4. This is the equivalent circuit of eral percent. This allows a reasonably accurate prediction of the transformer reduced to the primary circuit. In this cir- energy losses in the accelerator elements, which is of impor- tance in designing setups operating with a high repetition rate for a long period of time.

3. PULSE FORMING LINES

3.1. Using coaxial forming lines of conventional type While choosing the electrical and geometrical parameters of Fig. 4. Equivalent circuit of the transformer reduced to the primary circuit. the forming line, the value of the energy stored, energy

In particular, at a ϾϾ 1, that is, where RLoad ϾϾ r0,lnbϷ1. For a coaxial line with oil insulation, this corresponds to 102 rFL Ϸ 40 V.Ata,,1, we have ln b Ϸ a and rFL Ϸ 102 ~r0RLoad ! . For a Ϸ 102 ~« Ϸ 2.25, RLoad Ϸ 20 V!,it follows from the above expression that ln bϷ102 and rFL Ϸ r0 02 ϭ RLoad . For RLoad Ϸ 100 V~aϷ2.5!, the optimum impedance of the forming line is rFL Ϸ0.765r0 which makes rFL Ϸ 30 V for oil insulation. The efficiency of energy transfer for the optimum forming line impedance is given by the formula

32a 2 h ϭ . ~3! @a ϩ ~a2 ϩ 4a!102#3

Figure 6 shows the optimum forming line impedance ~a! and the corresponding efficiency of energy transfer ~b! versus the load impedance for an oil-insulated forming line. It follows from these considerations that for a coaxial forming line with oil insulation, the most optimum load impedance is 20 V.

3.2. Using spiral forming lines The length of a forming line is proportional to the pulse width. Hence, producing voltage pulses of increased widths ~hundreds of nanoseconds! would require utilization of ex- tremely long forming lines. Actually, to produce a 100-ns pulse in an oil-insulated pulse forming line the latter must ϭ 0 ! be as long as lFL tp c 2 «'10 m. The use of high- permittivity liquid dielectrics ~water, alcohol, or glycerin! Fig. 5. Current and voltage in the circuits of the Tesla transformer: allows a decrease in the length of the forming line. Such a: voltage across the primary capacitor, b: current in the primary circuit, c: voltage of the forming line. dielectrics, however, possess much higher conductivity than transformer oil and therefore the charging time should be

losses during its charging, and also the specific conditions of the formation of voltage pulses should be allowed for. In most cases where such generators are used, the load impedance RLoad can be considered as given. The maximum value of the cathode potential wLoad of the vacuum diode in a wide range of RLoad can be achieved only if there is a mismatch between the forming line and the vacuum diode. This causes a decrease in the efficiency of conversion of the energy stored in the forming line to the electron beam energy, and also the emergence of a sequence of reflected pulses. Further considered is a coaxial line of specified external radius r2 loaded onto a resistance RLoad . The wave impedance of such a line is rFL ϭ r0 ln b, where b ϭ r 0r , r is the radius of the central conductor of the 2 1 1 ! ! coaxial line, r0 ϭ 600 « @V#. For oil insulation, « ϭ 1.5 and r0 ϭ 40 V. Given the maximum electric field in the line Emax, the radius r2 of its outer conductor, and the load a ϭ 0 RLoad r0, the maximum value wLoad is achieved providing: Fig. 6. Optimum forming line impedance ~a! and the corresponding efficiency of energy transfer ~b! versus load impedance for oil type insulation ln b ϭ @~a 204! ϩ a#102 Ϫ ~a02!. ~2! of forming line.

decreased to a level of a few microseconds, which results in The spiral forming line can be charged with the use of a a considerable increase in pulsed charging currents and in Tesla transformer. One of the simplest ways of combining a energy losses during the time the line is charged. Moreover, spiral line and a Tesla transformer is shown in Figure 8. In with an optimum forming line geometry, an increase in « this case, the forming line of the high-voltage generator causes a decrease in its wave impedance and the efficiency should be made in the form of two series-connected lines. of energy transfer from the forming line into the load thus One of the lines is a spiral line of length lSL and another one drops. with a built-in Tesla transformer is a conventional coaxial One of the possible ways of solving this problem is to use forming line of length lCL. a spiral forming line. In this case, the forming line is an Most of the energy is stored in the spiral forming line. To ordinary forming line whose inner conductor is made of improve the operating conditions of the secondary coil of helically curled conductors ~Fig. 7!. the Tesla transformer, the electric field at the central con- The duration of pulses formed by the line depends on the ductor of the line CL should be as low as possible. Given the spiral pitch. The pulse duration factor ~coincident with the charging voltage of the spiral forming line, the minimum slowing-down ratio of the electromagnetic wave with re- electric field in the Tesla transformer will be achieved pro- spect to a conventional forming line! is viding r 0r Ϸe. In terms of the efficiency of energy transfer 2 1 ! into a load, the ratio r2 0r1 for the spiral line is close to e.To ~1 Ϫ ~r 0r !2 !{~p{r 0S!2 form a pulse with a clearly defined plateau in the load, the ϭ ϩ 1 2 1 ks Ί1 2 , wave impedances of the coaxial line and spiral line of the ln~r2 0r1! Tesla transformer, rCL and rSL, should be equal. In this case, Ϸ where S is the pitch of a spiral. The wave impedance of the the slowing-down ratio of the spiral line ks 2. With un- equal wave impedances ~normally, rSL Ͼ rCL!, a pulse with line is proportional to the value of ks while the pulse energy remains constant: an overshoot is formed in the load. The overshoot amplitude is determined by the relation ~rSL ϩ RL!0~rCL ϩ RL! and the S overshoot duration by the double electrical length of the tp ϭ ks tp coaxial line of the Tesla transformer.

rSL ϭ ks rCL. When a voltage dump wave propagates along the spiral forming line, an electric field with a longitudinal component Thus, keeping the forming line geometry optimum in Ez arises. This field may result in a breakdown between two terms of electric strength, it is possible to increase the effi- adjacent conductors of the line.As demonstrated by Gubanov ciency of energy transfer to a high-impedance load. Given et al. ~2002!, to preclude this breakdown, it is necessary to the slowing-down ratio ks, the external radius r2, and the make the central conductor of the spiral line in the form of a breakdown electric field at the inner conductor Emax~r1!, the multiturn spiral. The number of conductors of the line should voltage across the specified load RLoad is maximum, provid- be much greater than unity. This ensures a more uniform ing equality ~2! holds true. In the case of a spiral line, a ϭ field Ez and a decrease in electric field between adjacent RLoad 0r0 ks. The efficiency of energy transfer from the conductors that fully eliminates the interturn breakdown. forming line into a load is determined by expression ~3!. With ϭ 102, ϭ ϭ 1, which corresponds to a h~a! h~a!max 4. GAS GAP SWITCH ln~r2 0r1! ϭ102 or to the case of full matching. In particular, when using transformer oil as the insulation, the optimum The SINUS accelerators use a gas gap switch as the high- ! ratio of the radii at ks Ϸ 5 and RL Ϸ 100 V is e and the voltage switch. With high pulse repetition rates, when there efficiency of energy transfer from the spiral line into the is a need to have relatively short relaxation times and fast load h~a! Ϸ 1. Under the same conditions, the maximum disposal of spark combustion products from the discharge efficiency of energy transfer from the coaxial line into the gap, gas gaps possess some advantages. The early attempts load is merely 0.7. to increase the pulse repetition rate of the high-current accelerators failed. The main reason for the failure was the

Fig. 8. Combination of spiral forming line with a section of conventional Fig. 7. Spiral forming line. forming line allowing charging by a built-in Tesla transformer.

high instability of operation of the high-voltage gas switch. required to form a spark is higher than that in the self- For the single-shot operation, the instability ~RMS! of break- breakdown regime. down voltage is normally a few percent of an average value, Figure 10 shows schematically the time diagram for the and for a pulse repetition rate fr . 10 Hz, this value is main voltages in the gas gap switch. When a triggering pulse 10–20% and more. According to experimental results Smain is applied to the main switch S of the Tesla transformer ~Eltchaninov et al., 1979; Gubanov et al., 1997!, during the circuit ~Fig. 2!, the charging of the forming line begins operation of the setup in the repetitive regime, a region with ~waveform c, Fig. 5!. A negative voltage across the elec- a reduced electric strength of the gas appears in the inter- trode A increases with a typical time of TFL. Allowing for a electrode gap. The position of this region changes because delay of DTr , the pulse Strig triggers the main switch of the of gas convection. This region causes substantial instability trigatron control voltage generator. The voltage UTr across of the gas gap switch operation. This effect is found at pulse the controlling electrode C increases with a characteristic repetition rates higher than several pulses per second. The time of TTrig. This time is much shorter than TFL, which is SINUS setups use forced gas circulation between the elec- why the conditions for the gap to break set in rather fast. trodes to eliminate this effect. The gas velocity allows shift- This leads to stabilization of the gap operating voltage Ubreak. ing the main portion of the gas in the interelectrode space Changing the delay time DTr allows electronic tuning of within the time between pulses by nearly the same value as Ubreak. With a given gap geometry, the minimum operating the electrode radius so that the properties of the gas portion voltage of the gap Umin is determined by the maximum al- no longer affect the switch operation. lowable controlling voltage UTr and the maximum operating A three-electrode gas gap switch with electric field dis- voltage is limited by the self-breakdown voltage of the gap tortion ~a Trigatron! allows one to improve the reproducibil- Uself ~Fig. 10!. ity and to obtain a lower jitter of the operation and electronic The above principle of switching may be called “time control of the breakdown voltage. A schematic of the switch reference.” In practice, with this method, the reproducibility geometry is given in Figure 9. of the operating voltage of the gap is affected by possible In the case of fast distortion of the electric field near the instability of the voltage across the primary store C1 at the central electrode C of the trigatron, the discharge gap breaks moment the main switch Smain operates. Indeed, if the volt- down when applying a positive high-voltage triggering pulse age across C1 changes, the forming line charging rate also to it. At the moment the field strength near the electrode C changes. Hence, by the moment Strig, the forming line volt- exceeds the electric strength of the gas, a spark channel is age is different. In this case, another method for stabilizing formed between the electrodes A and C and the potential of the electrode C equals that of the electrode A. In what follows, the gap B–C breaks down, thus completing the switching process. Experiments demonstrate that in the case of such a controllable breakdown the load pulse rise time is somewhat longer than that found in the self-breakdown regime. For example, for a gap spacing of ;3cmandagap pressure of ;16 atm, the pulse rise time in the self-breakdown regime is 3–5 ns and in the controllable regime it is 6–10 ns. This indicates that in the controllable regime, the energy

Fig. 10. Time diagram of gas gap switch voltages: Smain: Triggering pulse for the main switch of the Tesla transformer, Strig: Triggering pulse for the Fig. 9. Typical geometry of the trigatron gas gap switch: A: Forming line main switch of the trigatron, UFL: charging voltage of the forming line, UTr : electrode ~negative!, B: Transmission line electrode ~initially grounded!, Controlling voltage ~electrode C!, Ubreak: breakdown voltage of the gas C: Controlling electrode ~positive!. gap, Uself : self-breakdown voltage of the gas gap.

Ubreak is preferable. Its main point is the use of a fast com- the cathode surface ~Mesyats & Proskurovsky, 1989; Mes- parator, which produces triggering pulse Strig at the instant yats, 2000!. Electrons are emitted from the dense surface the forming line voltage reaches a preset level. We can call plasma having almost unlimited emission capacity, which this method “level reference.” In this case, the reproducibil- allows particle density as high as 1014–1017 cmϪ3 in the ity of Ubreak is much less affected by the primary store volt- extracted beam. High reproducibility of cathode plasma is age instability, since the latter is basically transformed into advisable to generate electron beams in a repetitive regime. a jitter of the operation of the gas gap switch. As found in the experiment ~Gunin et al., 2000!, cathodes Thus, by changing the position of the triggering pulse of made from pure metals ~e.g., Cu, Mg, or stainless steel! the trigatron generator, it is possible to change the level of rather rapidly lose the capability for efficient emission. The the breakdown voltage of the gas gap switch in some range delay time of the diode current grows, and the peak value of current decreases with the number of pulses made. Thus, for Ϫ Umax Umin copper and stainless steel cathodes, the current delay time Dbreak ϭ {100%, Umax was found to approach the voltage pulse width ~;20 ns! during 104–105 pulses. Emission from a stainless steel cath- which can be called the range of control of the switch. Here, ode completely ceased after 106 pulses. Umax Ϫ Umin are the limiting values of the charging volt- The same experiments revealed that cathodes made from age of the forming line at which the breakdown occurs due the pyrolytic graphite possess the best-known durability and to distortion of the field by the potential across the electrode emission uniformity when producing tubular electron beams 0 2 C. The value Umax is close to the self-breakdown voltage of with ;20 kA cm current density. For these cathodes, the the switch. The value Umin is determined by the degree to current delay time was found to increase from zero up to a which the electric field is distorted near the surface of the few nanoseconds and saturate during the first 5{106 pulses. electrode C. The gap A–C breaks down at some critical This is the time a specific shape of the cathode edge is value of Ebreak, which is the superposition of the fields in- formed, resulting from the material erosion. Further, the duced by the electrodes A and C: emitting properties of the cathode and the diode current do not change during at least 108 pulses.An electron diode with

Ebreak ϭ EA~UFL ! ϩ EC ~Utrig !. graphite cathode was employed in a high-power X-band microwave generator based on relativistic backward-wave The curvature radii of the electrodes A and B are much oscillator. The electron beam was transported in a magnetic larger than the gap spacing in the gas gap switch. Therefore, field ~;0.7 T! produced by a DC solenoid. The power of the the field EA is inversely proportional to the switch gap spac- microwave pulses was ;450 MW, with a ;7-ns pulse width ing. The radius of the electrode C is much larger than the ~FWHM!. The pulse repetition rate was 100 Hz. The peak 8 switch gap and therefore the field EC is inversely propor- power of microwave pulses did not drift during 10 pulses. tional to the curvature radius of the electrode C. Decreasing Figure 11 shows 30 consequent pulse samples whose rather the radius of the electrode C causes an increase in field EC high reproducibility attests to stable operation of the entire and, consequently, broadens the range of control of the op- source after 108 pulses ~Gunin et al., 2000!. erating voltage Dbreak. The maximum range of control ob- tained on the SINUS-500 setup is 75%. However, with small radii of rounding the electrode C ~;1–2 mm! the latter is worn in rather rapidly ~105–106 pulses!. In this case, the electrode C should be replaced to recover the range of control of the switch. Therefore, for switches with a lifetime of 107–108 pulses, a larger radius of curvature of the electrode C ~3–4 mm! is chosen. The range of control Dbreak in this case makes up 30–50%.

5. PRODUCTION OF ELECTRON BEAMS The SINUS setups are direct-action accelerators. This means that, when producing electron beams, the accelerating voltage is applied immediately to the gap of an electron diode. The SINUS accelerators are employed to produce intense solid electron beams in planar diodes and annular beams in coaxial magnetically insulated diodes. With that, cold explosive-emission cathodes are used. A typical rise time of the diode voltage is 1–10 ns, which gives good conditions Fig. 11. Typical waveforms of ~a! diode voltage, ~b! beam current, and for the development of the explosive electron emission from ~c! microwave power after 108 pulses.

Production of solid electron beams with current densities 6. PULSED CHARGING OF THE of 10–100 A0cm2 with high spatial uniformity in a planar PRIMARY ENERGY STORE OF A diode requires provision of numerous emission centers si- SINUS ACCELERATOR multaneously emerging over a large cathode area. Krasik et al. ~2001! studied the plasma luminescence accompany- The electric power consumed by a SINUS setup in repetitive ing the generation of the cathode emission centers using a regime may range to a few hundreds kilowatts. To fast and 4Quick05A fast framing camera ~;5-ns frames!. Metal- efficiently charge the primary capacitive energy store C1 of ceramic, velvet, corduroy, carbon fiber, and carbon fabric the Tesla transformer ~Figs. 2, 4!, a pulsed circuit schemat- cathodes were examined. It was observed that the emission ically depicted in Figure 12 is used. centers emerge during the front of the voltage pulse. Both The key elements of the circuit are the power thyristor the number of the centers and the delay time of the emission switches Sr and Sc. These thyristors are triggered in turn were found to depend on the rate of electric field applied to during the charging cycle of the primary capacitor C1. The the cathode. Cold cathodes stressed to E ϭ 25–65 kV0cm gas gap switch GS operates at the instant the main thyristor and dE0dt ϭ 0.5–2.5 kV0~cm{ns! did not allow production S of the Tesla primary ~Figs. 2, 4! is in closed state ~Tbreak in of low-divergence electron beams because of the discrete- Fig. 5!. At this moment, the time derivative of the current ness of the cathode plasma. flowing in the switch S discontinues ~Fig. 5b!. At the mo- Parameters of voltage pulses produced by the SINUS ment of Topen, the current in the Tesla primary changes its accelerators are notably ~about an order of magnitude! over sign and the switch S opens. Thus, by the moment the charg- the above mentioned limits. This allows rather uniform dis- ing of the capacity C1 starts, its voltage is equal to some ϭ 20 tribution of current in the electron beams generated. Thus, negative value Ur ~Fig. 5a!. The energy Er C1 Ur 2isthe Bykov et al. ~1995! studied metal-dielectric cathodes. The residue of the energy initially stored in the capacity C1. 2 area of the cathode emission surface was ;200 cm , the Triggering of the switch Sr starts the process of recharging diode voltage and current were ;500 kV and ;5 kA, re- of the capacity. As the current flowing in the Sr–L1–C1 cir- spectively, with ;20-ns pulse width. The spatial nonunifor- cuit changes its sign, the switch Sr opens and a positive mity of electron current was no worse than 20%. The cathode voltage close to Ur remains in the C1 capacity. The residual 8 demonstrated successful operation during 10 pulses in a energy Er is recuperated to use in the next operation cycle. continuous regime with a pulse repetition rate of 100 Hz. As the switch Sr opens, a triggering pulse is given to the Thin-blade cathodes ~e.g., metal-dielectric ones! were switch Sc. A current starts flowing in the Cf –Sc–L2–C1 cir- found to possess lesser sensitivity of impedance to the cath- cuit and outcharging of the capacity C1 to the initial level of ode plasma expansion and, hence, improved impedance sta- U1 occurs ~Fig. 5a!. Thus, the sequence of triggering pulses bility during a nanosecond pulse ~Belomyttsev et al., 1999!. during one operation cycle of the accelerator is: Main, Triga- They were applied to produce solid electron beams with tron, Recuperator and Charge. The time for one cycle is ;200 A0cm2 current density to feed S-band and L-band usually less than a few milliseconds. This allows the maxi- vircators ~Korovin et al., 2003, this issue!. mum pulse repetition rate of several hundreds hertz. A high

Fig. 12. Schematic of power supply of a SINUS accelerator.

Q factor of the recuperation and outcharging circuits allows one to have minimum active losses in the pulsed power source.

7. USING MOLECULAR CAPACITORS FOR THE PURPOSE OF ENERGY STORAGE IN POWER CIRCUITS OF SINUS ACCELERATORS The specific energy density of the modern molecular capacitors reaches ;3.8 MJ0m3. This high value ranks them with the chemical batteries and allows the development of compact energy sources on their base. Unlike the conventional capacitors, the molecular capacitors have a rather high internal resistance. However, this did not prevent their successful application in a series of pulsed power problems. An example is the storing banks for some of the SINUS machines operating in the batch repetitive mode. In some cases, Fig. 13. Stabilization of currents in the solenoid sections using a PWM molecular capacitors were used to feed both an accelerator controller. and a powerful quasi-DC solenoid producing a guide magnetic field for the electron beam transport.

Expression ~4! assumes that the internal resistance R0 of a 7.1. Feeding a powerful magnetic coil molecular capacitor is a lumped constant value. However, proper examination shows that the internal properties of The paper by Grishin et al. ~2001! describes the operation of such a capacitor are equivalent to some discrete cellular a power supply designed to feed a two-sectional solenoid structure ~Fig. 14!, with the number of cells N .. 10. The with a 360-kW power consumption and 1.2-kA full current. cell parameters Ci , Ri are constant and may be found, for The maximum magnetic field induction was 1.6 T. The en- example, from the conditions ergy store based on molecular capacitors provided quasi-DC operation of the coil during 1-s pulses. The solenoid was C 1 U ϭ 0 ϭ max switched into the capacitive store by a switching current Ci , Ri { , N N Imax regulator assembled from isolated-gate bipolar transistors ~IGBTs; Bees & Tydeman, 1999!. Controlling the switch where Umax is the rated maximum charging voltage of the with a PWM controller allowed a rather small decrease in capacitor and Imax is its rated short-circuit current corre- the solenoid current during the pulse ~less than 2%! while sponding to this voltage. The relation between Ci and Ri the voltage across the store was decreasing from 660 V to depends on the capacitor inner construction and, therefore, 300 V. Figure 13 shows the typical waveforms of currents on its specific mark. Therefore, designing a bank of molec- flowing in the solenoid sections. ular capacitors requires examination of a concrete capacitor In this regime, a constant current I0 is consumed from the sample. molecular capacitor bank and the voltage across the load According to the equivalent circuit, consumption of the ~magnetic coil! having a constant resistance of RS equals to energy E initially stored in a molecular capacitor occurs ϭ 0 US I0{RS . gradually by sequential discharge of the elementary cells. Stabilization of the current is possible until the moment of This causes a rather rapid decrease in the voltage across the T0 when the bank voltage ~initially equal to U0! falls below capacitor occurring as a load is connected and its partial the level of US. Neglecting the energy stored in the solenoid gradual recovery as the load is disconnected. This results in inductance yields a substantial value of the residual energy Eres. This property, undoubtedly, impedes the energy consumption from the mo- C M 2 2 T0 ϭ @~U0 Ϫ R 0 I0 ! Ϫ US # , ~4! 2I0 Us

where CM and R0 are the capacitance and internal resistance of the molecular capacitor bank. As is seen from ~4!, for a given load power PS ϭ I0US , an optimum load resistance opt RS exists corresponding to a maximum time T0 of current stabilization. Fig. 14. Equivalent circuit of a molecular capacitor.

lecular capacitor, limiting the efficiency of energy transfer to the load

E0 Ϫ Eres h ϭ 1 Ϫ . ~5! E0

For example, in the case reported by Grishin et al. ~2001!, the solenoid resistance was close to the optimum one RS Ϸ opt RS , the voltage across the bank was halving during 1 s, and the energy consumption efficiency made up h'15%.

7.2. Feeding a SINUS accelerator

The above principle of operation of a pulsed power supply Fig. 15. Equivalent circuit of primary store charging. of a SINUS accelerator ~Fig. 12! assumes that the recuperator switch Sr is open at the instant the charging switch Sc is triggered. In this case, the time Tch of Sc switch triggering is is found using the method of successive approximations. Ͼ fixed and conforms the condition of Tch p!Lr C1. This This dependence is mapped in a form of two-dimensional classic method has one substantial drawback. The high val- lookup table, with typical dimension of 256 ϫ 256. The ues of the Q factor of all oscillatory circuits result in the fact master microcontroller measures the initial values of Uf and that, after operation of Sr and Sc switches, the final voltage Ur before recuperation in each operation cycle, finds the UC1 across C1 strongly depends on initial values of Ur and table value of Tch, and sets it to timer. Typical waveforms in Uf. The residual negative voltage Ur ~Fig. 5! depends, in Figure 16 illustrate how the C1 capacity is charged to a turn, on the gas gap switch operation voltage Ubreak. preset level of UC1. Wide-range ~;50%! control of gas gap switch operation The upper graph shows voltages Uf and U1 and the three voltage Ubreak using a trigatron generator, as well as batch lower ones show currents flowing in the switches Sr~I1! and operation of accelerator fed from a molecular capacitor bank ~characterized by Uf value gradually decreasing during the batch! require stabilization of the UC1 voltage final level in each cycle to provide normal operation in the next cycle. For this purpose, dynamic control of the switch Sc triggering time with respect to switch Sr triggering time was realized. Consider the equivalent circuit of primary store charging given in Figure 15. The circuit operation is described by the following set of equations:

'' R1 ' 1 1 I1 ϭϪ {I1Ϫ {I2Ϫ {I1 L1 L1{C1 L1{C1 ~6! Ά '' R2 ' 1 1 1 I ϭϪ I Ϫͩ ϩ ͪ{I Ϫ {I . 2 2 2 1 L2 L2{Cf L2{C1 L2{C1

The C1 charging current is I3 ϭ I1 ϩ I2, and the C1 voltage is ϭ 0 t U1~t! 1 C1{*0 I3~t!{dt. The initial conditions are ~the Sc switch is open and the Sr switch is closed!: U1~0! ϭ Ur , ϭ ϭ ϭ ' ϭϪ 0 ' ϭ Uf ~0! Uf , I1~0! 0, I2~0! 0, I1~0! Ur L1,I2~0! 0. At the moment of Sc operation, the conditions are redefined. The opening state of Sr and Sc switched is simulated by ' ' redefining the L1 and L2 parameters and I1 and I2 deriva- tives. Integration of system ~6! using Runge–Kutta method gives the dependence for the final value of C1 voltage, UC1 ϭ F~Uf ,Ur ,Tch!. Then, for some preset value of UC1, the dependence

Fig. 16. Stabilization of the primary store voltage by means of dynamical ϭ Tch f ~Uf ,Ur !~7!tracking of currents in the recuperation and charging switches.

Table 1.

Electron Trigatron Beam Pulse Rep. Time of Accelerator energy, control current, width, rate, continuous Size, Weight, name keV of voltage kA ns Hz operation cm tons

SINUS-120 200 No 2.0 4 1000 20 min л14 ϫ 80 0.05 SINUS-160 300 No 3.0 4.5 100 no limit 40 ϫ 70 ϫ 70 0.1 SINUS-200030 250 No 2.5 30 200 30 min л22 ϫ 160 0.25 SINUS-200 200 No 5.0 10 50 no limit 80 ϫ 30 ϫ 220 0.3 SINUS-400 500 Yes 5.0 14 150 no limit л50 ϫ 500 0.7 600 6.0 22 150 no limit SINUS-500 Yes л55 ϫ 500 0.8 550 5.5 22 400 30 min SINUS-5000C 600 No 6.0 26 100 1 s л55 ϫ 500 0.8 SINUS-700 800 Yes 8.0 30 200 20 min л80 ϫ 800 3.5 SINUS-888 1000 Yes 9.0 20 100 1 s л80 ϫ 700 3.0 SINUS-7000130 650 No 4.8 130 100 1 s л80 ϫ 600 4.0 SINUS-700090 450 Yes 7.5 90 200 2.5 s л80 ϫ 600 4.5 2000 20.0 50 0.1 no limit SINUS-7 No л140 ϫ 1200 10.0 1500 15 50 100 15 min

Sc~I2! and C1 charging current ~I3!. The voltage across Cf The SINUS-160 setup ~Fig. 17! was employed to produce varies in the range of DUf and the negative voltage across high-voltage pulses in an UWB source operating in a con- C1 varies in the range of DUr . The time Tch varies from 0 tinuous regime with a pulse rate of 100 Hz ~Andreev et al., up to Tmax. The waveforms ~a! corresponds to Tch ϭ Tmax, 2003, this issue!. The machines SINUS-5000C and SINUS- ~c! Tch ϭ 0, and ~b! to some intermediate case. 700090 ~Fig. 18! have an autonomous power supply from The above method of voltage stabilization in the Tesla molecular capacitors. The SINUS-400 and SINUS-5000C transformer primary was realized in the construction of the are mounted in individual mobile containers. They are used SINUS-700090 accelerator. The stabilization allowed both to produce electron beams in pulsed X-band microwave feeding the accelerator from a bank of molecular capacitors sources 600–800 MW output powers. The SINUS-400 setup when operating in batch repetitive regime and electronic was used in experiments on nanosecond radio location. Based tuning of gas gap switch operation voltage with 50% depth on the SINUS-7 accelerator, single-mode microwave sources ~Dbreak!. Instability ~RMS! of the C1 voltage level was not with record powers were developed: ;3 GW X-band con- worse than 1%. The pulse repetition rate was 200 Hz and the ventional relativistic BWO ~Gunin et al., 1998; Batrakov pulse batch duration was 2.5 s. The power consumed from et al., 2001! and ;5 GW S-band resonant BWO ~Korovin the molecular capacitor bank during the batch was 150 kW. et al., 2003, this issue!. Stabilization of the primary voltage allowed the setup oper- A capability for repetitive operation with high ~10– ation with more than a twofold decrease of input voltage 100 kW! average powers of electron beams is the main ~Uf ! during the batch. The efficiency of the bank energy use ~5! was as high as h'50%.

8. BASIC PARAMETERS OF THE ACTIVE SINUS ACCELERATORS During the period of 1990–2002, more than 10 SINUS accelerators were developed at the IHCE. Table 1 shows the basic features of these machines. The accelerators are con- ventionally used in the following applications: • Production of high-power microwave pulses and ultrawideband ~UWB! pulses; • Electron beam technologies with beam output in atmosphere; • Studies of high-power microwave effects in biological objects ~Bol’shakov et al., 2000!. The accelerators SINUS-200030, 7000130, and 700090 use a pulse forming line of spiral type ~see Section 3, Fig. 8!. Fig. 17. High-voltage generator SINUS-160.

Table 2.

max max min min max max Ee , WFL, r2 , lFL , tp , fr , P , MeV J cm cm ns Hz W

0.1 1 5 25 2.5 105 105 1103 50 250 25 2.5{103 2.5{106 10 106 500 2500 250 50 5{107

max @ Ϫ203 yields fr WFL . The maximum average power is max @ max proportional to pulse repetition rate, P fr . Table 2 presents some data characterizing potentialities of Tesla transformer forming line charging. The accelerators of the SINUS type have shown them- Fig. 18. Accelerator SINUS-700090. selves to be reliable long-lived sources of intense electron beams. During years, they are successfully used as a tool of research in high-power electronics. The totality of the parameters of the setups is unique, which allows them to hold distinctive feature of most of the SINUS machines. Devel- a lead in pulse power technology over the world. opment of a repetitive accelerator requires resolving the problems of its operation stability and lifetime. The RMS pulse-to-pulse amplitude spread of the SINUS machines is, REFERENCES as a rule, not over 3%. Trigatron control of gas-gap switch operation in combination with forced gas circulation allows Andreev, Yu.A., Gubanov, V.P., Efremov, A.M., Koshelev, decreasing this level to less than 0.5%. The trials performed V.I., Korovin, S.D., Kovalchuk, B.M., Kremnev, V.V., for the SINUS-500 ~Fig. 19! accelerator evidenced that the Plisko, V.V., Stepchenko, A.S. & Sukhushin, K.N. ~2003!. High-power ultrawideband radiation source. Laser Part. Beams lifetime of the whole setup is over at least 3{108 pulses. 21, 211–217. Batrakov, A.V., Karlik, K.V., Kitsanov, S.A., Klimov, A.I., 9. CONCLUSION Konovalov, I.N., Korovin, S.D., Mesyats, G.A., Ozur, G.E., Pegel, I.V., Polevin, S.D., Proskurovskii, D.I. & According to aforesaid ~see Section 2!, it is easy to make Sukhov, M.Yu. ~2001!. Increasing of pulse duration of the quality estimation of a SINUS machine main parameters relativistic microwave BWO with output power 3 GW. Tech. according to the value of energy WFL stored in the pulse Phys. Lett. 27, 150–152. max forming line and the maximum electron energy Ee . The Bees, G.L. & Tydeman, A. ~1999!. Capacitor charging power condition of high efficiency of the line charging sets a cor- supply design for high pulse repeatability applications. In Proc. max 12th IEEE Pulsed Power Conf. Monterey, CA, pp. 397–398. relation between the forming line external radius r2 and its minimum length l min defining the minimum pulse length Belomyttsev, S.Ya., Korovin, S.D. & Pegel, I.V. ~1999!. Ef- FL fect of expanding explosive-emission centers plasma on the ~tmin @ l min!. The maximum pulse repetition rate is limited p FL impedance of high-current diode. IEEE Trans. Plasma. Sci. 27, @ 203 by the time of the forming line charging tch WFL , which 1572–1577. Bol’shakov, M.A., Evdokimov, E.V., Goncharik, A.O., Bugaev, S.P., Gunin, A.V., Klimov, A.I., Korovin, S.D., Pegel, I.V. & Rostov, V.V. (2000). Biological effects of repetitively-pulsed high-power microwave radiation. Book of Abstracts, EUROEM- 2000, 30 May–2 June 2000, Edinburgh, p. 99. Bykov, N.M., Gubanov, V.P., Gunin, A.V., Korovin, S.D., Kutenkov, O.P., Landl, V.F., Polevin, S.D., Rostov, V.V., Mesyats, G.A. & Zagulov, F.Ya. ~1995!. Development of long-lifetime cold cathodes. In Proc. 10th IEEE Pulsed Power Conf. Albuquerque, NM, pp. 71–74. Eltchaninov, A.S., Zagulov, F.Ya, Korovin, S.D., Landl, V.F., Lopatin, V.V. & Mesyats, G.A. ~1983!. Accelerators of high-current electron beams with high pulse repetition rate. In High-Current Electron Beams in Technology, pp. 5–21. Novosi- birsk: Nauka. ~in Russian!. Eltchaninov, A.S., Zagulov, F.Ya, Korovin, S.D. & Mesyats, Fig. 19. High-power microwave pulse source SINUS-500. G.A. ~1979!. Electron beam accelerator with high pulse recur-

rence frequency. Proc. of the 3rd Int. Conf. on High Power Gunin, A.V., Klimov, A.I., Korovin, S.D., Pegel, I.V., Polevin, Electron and Ion Beams. Novosibirsk, Russia. Vol. 1, 191–197. S.D., Roitman, A.M., Rostov, V.V. & Stepchenko, A.S. & Eltchaninov, A.S., Zagulov, F.Ya, Korovin, S.D., Mesyats, Totmeninov, E.M. ~1998!. Relativistic X-band BWO with 3 G.A. & Rostov, V.V. ~1981!. High-current repetitively-pulsed GW output power. IEEE Trans. Plasma Sci. 26, 326–331. electron accelerators for microwave production. In Relativistic Gunin, A.V., Landl, V.F., Korovin, S.D., Mesyats, G.A., Pegel, High-Frequency Electronics ~Gaponov-Grekhov, A.V., Ed.!, I.V. & Rostov, V.V. ~2000!. Experimental studies of long- pp. 5–21. Gorky: IAP AS USSR. ~In Russian! lifetime cold cathodes for high power microwave oscillators. Grishin, D.M., Gubanov, V.P., Gunin, A.V., Korovin, S.D. & IEEE Trans. Plasma. Sci. 28, 537–541. Stepchenko, A.S. ~2001!. A power supply for one-second Korovin, S.D., Kurkan, I.K., Loginov, S.V., Pegel, I.V., source of highly-stable magnetic field. In Proc. IEEE Pulsed Polevin, S.D., Volkov, S.N. & Zherlitsyn, A.A. ~2003!. Power Plasma Science Conference (PPPS-2001). Las Vegas, Decimeter-band frequency-tunable sources of high-power mi- NE, pp. 1638–1641.1641. crowave pulses. Laser Part. Beams 21, 175–185. Gubanov, V.P., Gunin, A.V., Korovin, S.D. & Stepchenko, Krasik, Ya.E., Dunaevsky, A., Krokhmal, A., Felsteiner, J., A.S. ~2002!. Repetitive nanosecond high-voltage generator Gunin, A.V., Pegel, I.V. & Korovin, S.D. ~2001!. Emission based on spiral forming line. Pribory i Tekhnika Eksperimenta properties of different cathodes at E Յ 105 V0cm. J. Appl. Phys. (Rus.) 1, 73–75. 89, 2379–2399. Gubanov, V.P., Korovin, S.D., Pegel, I.V., Roitman, A.M., Mesyats, G.A. ~2000!. Ectons in vacuum discharge. Moscow: Rostov, V.V. & Stepchenko, A.S. ~1997!. Compact 1000 pps Nauka. high-voltage nanosecond pulse generator. IEEE Trans. Plasma Mesyats, G.A. & Proskurovsky, D.I. ~1989!. Pulsed Electrical Sci. 25, 258–265. Discharge in Vacuum. Berlin–Heidelberg: Springer-Verlag.