Double Pulse Generator for Unipolar Discharges in Long Plasma Tubes for the AWAKE Experiment

High-voltage pulsed gas discharges can produce suitable plasma for wakefield particle acceleration experiments. Such plasmas are challenging loads characterized by significant parasitic elements and fast impedance transitions leading to hard-to-predict dynamic behavior. This hinders the use of solid-state pulse generators to replace inefficient and limited lifetime spark gaps or thyratrons. This article presents the development, simulation, and test of a new semiconductor-based double pulse generator for a 5-m-long plasma load. It uses two successive pulses. The first one consists of a step-up inductive discharge and leads to a low current arc (10 A) enough to set the plasma to a low impedance state. The second pulse, generated by a capacitive discharge, increases the arc current up to 400 A. The pulses are generated by two subcircuits integrated together and tested, showing a substantial reduction of the required instantaneous power compared with the one needed using a single pulse and resulting in a high ionization fraction gas discharge pulse with nanosecond jitter.

, flash-lamps [5], and particle accelerators [6].The latter is the main purpose of the circuit presented in this article.Plasma acceleration occurs in an electron density wave generated by an intense laser pulse [7] or by a charged particle bunch [8] and can potentially sustain electric fields 1000 times larger than conventional radio frequency particle acceleration cavities [7].The Advanced Proton Driven Plasma Wakefield Acceleration Experiment (AWAKE) [6], [9] uses proton bunches to generate a wakefield able to accelerate electrons with an energy gain of up to 0.2 GeV/m [10].
The current AWAKE's plasma source principle by laser field ionization [11] cannot be indefinitely extended in length due to the laser beam diffraction and an alternative length scalable source is required to achieve higher particle beam energies.Two technologies are being considered for the next stages of the AWAKE experiment [12], a helicon plasma source [13], and a discharge plasma source.The latter requires the application of high-voltage and high-current electric pulses able to ignite and heat long plasma sections.In this article, we present a double pulse generator designed for this purpose.
The double pulse generator is designed to efficiently handle the wide dynamic range of the plasma load characteristics, and therefore, it is composed of two coupled subcircuits: a step-up inductive discharge ignition circuit that produces voltage pulses with amplitudes up to 120 kV at currents over 10 A, much higher than the typical plasma breakdown voltages; and a capacitive discharge heater subcircuit, which increases the plasma current to more than 400 A while using a voltage of up to 10 kV.The double pulse feature assures a highly reproducible high-current plasma discharge, which is the main objective of the circuit.

A. Gas Discharges
Plasmas can be created in low-pressure gases by unipolar direct current discharges between two electrodes when a voltage difference larger than the breakdown voltage is used [14].The typical V -I characteristic curve of plasma discharges contains two reduced impedance regimes: glow discharges for mA currents and arc discharges usually above 1 A [15].Only the arc regime produces a significant ionization of the gas, which is necessary to attain the plasma properties required: an electron density in the order of 7 × 10 14 cm −3 with a longitudinal uniformity better than 0.25% over 10 m.To achieve this, the discharge is made inside a 5-m glass tube with 25-mm inner diameter, filled with the working gas at a variable pressure (1-50 Pa).To keep the plasma density cylindrically symmetric around the tube axis and uniform in length, a coaxial return cage is used (Fig. 1).This cage is attached to the anode and can be extended, along the tube, up to 35 cm from the cathode.The formed 35-cm-long gap, between the cathode and the anode cage extremity, sets the electric field for the electron emission from the cathode, reducing the breakdown voltage for long tube lengths.

B. Ignition and Heating
The duration of the pulse used to create the plasma is a compromise between applied voltage and density uniformity.Discharge durations longer than 100 µs are prone to density modulations [5].However, microsecond-short discharges require voltages much higher than the breakdown voltages used in continuous or long pulse discharges.For example, jitters of 1 µs and 1 ns were obtained with ignition voltages of 10 and 125 kV, respectively, for simple plasma geometries [16].
An ignition voltage in the range of 50-120 kV applied in the tube's cathode-anode gap is required to produce a nanosecond range jitter and 10-µs-long plasma.On the other hand, a high ionization fraction requires current densities of 50-200 A/cm 2 (0.25-1 kA for the 25-mm inner diameter tube).Combining these currents and voltages in the same pulse would result in a 120-MW peak power.To minimize this peak power, the pulse generator can be split into two lower power subcircuits.The high-voltage ignition circuit is used to start a low current (10 A) discharge.Having the arc discharge initiated (plasma ignition) and therefore establishing the plasma at a reduced impedance, it is possible to later increase the arc current, up to the kiloampere level, with a significantly lower voltage (10 kV) capacitive discharge.To prevent the development of spatial modulations in the plasma density, it is important to raise the heater current to the target value in a few microseconds, coping with the stray inductances, which typically requires a heater voltage of approximately 10 kV.The double pulse results in a maximum power usage of around 10 MW, therefore reducing the total power by a factor of approximately 10.
Section II contains a description of the design and operation of the double pulse generator as well as the sizing of its main elements.Section III presents PSpice simulations for the double pulse generator using a plasma model.Section IV contains the experimental results obtained from testing the double pulse generator.In Section V, the conclusions of this article are presented.

II. DOUBLE PULSE GENERATOR OPERATION AND DESIGN
To design the double pulse generator components, the operation of the circuit must be understood as well as the interplay between all the parts.The double pulse generator full circuit schematic presented in Fig. 1 is the merging of two subcircuits: 1) the step-up transformer-type negative high-voltage pulser [17] with grounded ignition switch S ign and 2) the negative pulse capacitive discharge circuit [18], with grounded heater switch S h , modified to adapt to both the dynamic plasma load and to make the merging of both circuits possible.

A. Circuit Operation
The operation of the double pulse circuit during one repetition period (T ) is decomposed into six subsequent steps (Fig. 2).Each step corresponds to a semiconductor switching scheme and related gas/plasma state.
The first step (Fig. 2, Step 1) happens when both switches (S ign and S h ) are in off position, and the ignition (C ign ) and the heater (C h ) storage capacitors are charged to the initial voltages (V ign and V h ).
The second step (Fig. 2, Step 2) starts when the ignition switch S ign turns on.The capacitor then discharges through the transformer primary winding.As the ignition diode D ign , on the secondary, is reverse biased, the transformer will store energy as core flux linked to the primary winding magnetizing Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.inductance L µ .This step lasts up to t p = 17.5 µs, with the primary current I p , rising to values up to 200 A.
The power supply V ign resistance R ign is too high to contribute to the I Lµ current.Therefore, the ideal primary circuit is an undamped resonant circuit, with impedance Z µ = (L µ /C ign ) 1/2 and resonance frequency ω r = 1/(L µ C ign ) 1/2 , where for ω r t ≪ 1, the current i Lµ and voltage V Cign can be approximated as V Cign = V ign cos(ω r t) In the third step (Fig. 2, Step 3), the ignition switch (S ign ) turns off, forward biasing the snubber D isn and the ignition D ign diodes.Considering the buck-boost equivalent of this step, operating in discontinuous conduction mode (DCM), the average voltage V Cisn across the snubber capacitor C isn will be approximately where δ = t p /T and δ D is the time fraction of the conduction of the snubber diode D isn with respect to the period T .The peak value V isnMax of the primary voltage is given as From ( 4), the transformer's primary voltage polarity is inverted, resulting in the forward biasing of the ignition diode D ign [19].The hold-off voltage V SignMax of the main switch S ign is The peak value of the voltage applied to the plasma tube V tube will be approximately where N 2 /N 1 is the transformer step-up ratio.However, the plasma is not generated instantaneously.The current rise in the secondary is limited by the transformer leakage and circuit stray inductances and by the charging of the tube's parasitic capacitance, prior to gas ignition.In Step 3, the ignition snubber on the primary side will absorb some of the transformer energy that cannot be delivered to the secondary.Typically, the time between switch-OFF and plasma ignition is 1-2 µs.The fourth step (Fig. 2, Step 4) starts when the plasma ignition occurs.The plasma impedance decreases rapidly, diverting nearly all the transformer energy away from the ignition snubber.The plasma current has a sudden spike and then drops slowly as the magnetic energy is discharged.
The fifth step (Fig. 2, Step 5) starts after the ignition current becomes nearly constant and the heater switch S h is turned on, typically 5 µs after S ign turns off.The injection of the high-current pulse heats the plasma producing a high ionization fraction of the gas as required for the application.The negative pulse capacitive discharge enforces a tube voltage of approximately Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
The sixth step (Fig. 2, Step 6) follows the heating phase, discharging through the conductive plasma and the residual magnetic energy stored in the transformer.Due to the inductance of the current path, turning off the heater switch S h will also activate the heater snubber, damping the overvoltage and protecting the heater semiconductors (switch S h and charging diodes).The inductor L h prevents the current from flowing through the charging diode.
The maximum repetition rate was set to 1 Hz, in adequation with the current requirements of the AWAKE project [9].The 1-Hz limitation allows the use of commercial compact power supplies for V ign and V h (around 250 W).If necessary, a safe high repetition rate (e.g., >10 Hz) requires a carefully designed cooling system for the circuit critical components such as the switches (S ign and S h ), diodes (D ign , D coup , D isn , and D hsn ), resistors (R c and R ptube ), and ignition transformer.The AWAKE experiment requires a plasma with unique parameters in the plasma acceleration landscape.Other plasma sources for lower energy particle accelerators (driven by short pulse lasers or electron beams) normally require higher density plasmas, much smaller plasma lengths and diameters as well as higher repetition rates [20], [21], [22].

B. Step-Up Storage Transformer Design
The pulse transformer was built following parasitic reduction (leakage inductance) and high-voltage insulation design principles [23].In this pulse generator, the energy stored in the transformer's equivalent magnetizing inductance must be considered as the criterium to select the core size and magnetic properties.The pulse transformer magnetizing inductance must be designed to store enough energy (around 7 J) to ignite the plasma.The secondary winding has to endure high voltages (up to 120 kV), which have voltage rise and fall times in the order of 10 ns (frequencies up to 200 MHz).Moreover, the pulse transformer core must not become saturated.
The first parameter of the pulse transformer to be sized is the equivalent magnetizing inductance (L µ ).Considering ideal circuit elements and semiconductors, a value of L µ = 350 µH can be computed from (1), using the input voltage V ign = 4 kV, a maximum ignition switch-ON time t pMax = 17.5 µs, and a magnetizing current of I pmax = 200 A.
To select a suitable magnetic core and number of primary turns (N 1 ) to achieve the above L µ value and energy, first consider that from Faraday's law, the ideal core maximum flux, i.e., the time integral of the primary per turn voltage, is given by the product of the core cross section (A Fe ) to the saturation flux density (B max ) as written in (8), where the product V ign t p was obtained from (1) considering I p(t=t p) = I pmax The magnetizing inductance (L µ ) is a function of the core dimensions A Fe , magnetic path length M gl , core permeability µ, and the number of turns N 1 squared [24] Replacing N 1 from ( 8) in ( 9) and rearranging terms, the equation relating to the core dimensions, core flux density, and magnetic permeability to the core energy is obtained With this relation, it is possible to select the pulse transformer magnetic core energy rating, defined as core volume (A Fe M gl ) multiplied by the core ratio B 2 max /(2µ).The magnetic core energy rating must equal the maximum magnetizing inductance energy L µ I 2 pmax /2.As the V tube voltage is required to reach 120 kV and the available V ign voltage is 4 kV, the buck-boost and pulse transformer must provide a step-up ratio of 30.Pulse transformers show increasingly high leakage inductances and parasitic capacitances for high step-up ratios.Therefore, moderate pulse transformer step-up ratios, N 2 /N 1 around 4, should be considered.This value would also enable reaching a secondary current (50-A theoretical maximum) high enough to set the plasma to a low impedance state.
To obtain 7 J of magnetic energy (L µ = 350 µH and I pmax = 200 A), from (10), the chosen core was Magnetic's Kool Mu toroidal core 0077165A7 (with M gl = 412 mm, A Fe = 987 mm 2 , B m = 1 T, and µ r = 22-from 50 kHz to 200 MHz).From ( 9), the number of turns was determined (N 1 ≈ 70).For a transformer step-up ratio of N 2 /N 1 = 4, the secondary winding must have N 2 = 280 turns.The secondary voltage will reach 120 kV if the turn-off primary voltage V isnMax given in (4) reaches −30 kV in the snubber sized in Section II-C.

C. Ignition RRCD Snubber Design
Snubbers are mainly used as semiconductor protection circuits.However, in this work, besides serving as protection, the snubber must also contribute to setting the buck-boost gain value V isnMax /V ign , as discussed in Section II-B, providing a pulse transformer primary voltage V isnMax around −30 kV [see (4)].Given the low pulse repetition rate (T ≈ 1 s), to limit the size of the capacitor C isn , the voltage V Cisn (3) across the snubber capacitor at beginning of Step 3 is nearly zero.Therefore, a resistor R isn must be added to the conventional RCD snubber circuit, resulting in the RRCD snubber.
From (4), supposing that V Cisn ≈ 0, to obtain V isnMax ≈ −30 kV, being The snubber capacitance of C isn is sized starting from the expression To have the pulse transformer primary voltage V isnMax set by R isn , during Step 3 ( t isn = 2 µs), the capacitor variation V Cisn should not be too high (less than 5% of V isnMax ).Considering a maximum capacitor voltage V Cisn = 0.05V isnMax ≈ 1.5 kV with mean capacitor current I Cisn = I pmax /2 = 100 A, the ignition snubber capacitance should be C isn ≈ 133 nF.The discharge resistance (R dis ) must be high enough to prevent the snubber capacitor from discharging Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
during Step 3, but low enough for that discharge to happen before the next pulse.Assuming a time constant much smaller than T , a resistance R dis = 200 k was selected.

D. Ignition and Heater Capacitor Design
The ignition storage capacitor C ign can be estimated by solving (2) to obtain C ign Considering 20% capacitor discharge (V Cign(t=t p) ≈ 0.8V ign ) the capacitance C ign is around 2 µF.
The storage capacitor C h should be sized to deliver the tube needed heater current I h ≈ 400 A, at V h ≈ 10 kV, during the heater pulse time t h ≈ 10 µs, considering again a 20% capacitor discharge The obtained capacitance is 2 µF.

E. Heater RCD Snubber Design
Due to the length of the plasma tube, the heater circuit will have a high parasitic inductance that will, at switch turnoff, generate a voltage spike (hard switching).The snubber is designed to protect the switch from this spike.The snubber capacitance is obtained from the following expressions: where V ShMax is the maximum voltage to be applied to S h and I hMax is the maximum current from the heater pulse Assuming an allowed peak voltage of V Shmax = 15 kV after the turn-off and a parasitic inductance of L htube ≈ 140 µH, at the maximum current of I ChMax = 400 A, the snubber capacitance should be C hsn ≈ 100 nF.The resistor R hdis = 100 k sets the snubber time constant value RC ≈ T /10, allowing a safe discharge of the snubber capacitance.
To prevent the turn-off voltage spike to activate the charging diode (GeneSiC's GAP3SLT33-214-14 in series), the L h inductor was placed From ( 16), considering V ShMax = 15 kV, t hsn = 1 µs (duration of the snubber activation), and I DchMax = 1 A (maximum allowed current for the charging diodes), the inductance calculated was 15 mH.With these values of R h , C h , and L h , the damping coefficient is high enough so that the capacitor charging is nonoscillant.

F. Switch and Diode Modules Design
Both switch modules use IXYS' IXBK55N300, selected by their fast switching and high voltage and current characteristics.The ignition switch S ign uses 13 insulated-gate bipolar transistors (IGBTs) in series to withstand a turn-off voltage in excess of 30, 2.3 kV per IGBT [25].The heater switch S h uses nine stages in series, each with three parallel IGBTs for 20-kV maximum current and near 400-A maximum current (Table I).The switch hold-off voltage is balanced using a resistive voltage divider and voltage clamping diodes (four series connected 1.5SMC530A) added in the collector-emitter terminals of each IGBT [26].The signal to trigger the IGBT gate is set by the NXP's DEVKIT-MPC5748G microcontroller and transmitted via fiber optics to a 500-V powered command board; 500 V is afterward distributed to all the IGBT stages through 1:1 galvanic isolation transformers.
Like the switch modules, the ignition and ignition-heater coupling diodes are composed of series-connected discrete diodes.The ignition module has 40 diodes (ST Microelectronics' STTH30S12W) and the coupling diode has 160 diodes (IXYS' DSEI120-12A), assuring the diodes hold-off safely the applied high voltages (4 kV × N 2 /N 1 = 16 kV for the ignition and 120 kV for the coupling diode).To guarantee static voltage balancing, each device has a parallel resistor sized from the diode's R eqOFF and V RRM parameters, as in [27] and [28].

III. SIMULATION OF THE DOUBLE PULSE GENERATOR
PSpice simulations are used to predict the behavior of the different components of the circuit and to verify the design of the double pulse generator.The essential system specifications are shown in Table I.
The parameters used for the simulation and the experimental discharges are presented in Table II.
The tube's parallel resistor (R ptube ) is used to dampen ignition current oscillations due to parasitic capacitance and inductance on the secondary.If R ptube resistance is too low, it increases the tube voltage rise time and may increase the jitter, but a too-high resistance will have no damping effect.A compromise value of 10 k was found to minimize the ignition jitter.The resistor R c limits the plasma discharge current, protecting the heater switch from overcurrent due to the plasma's negative impedance.

A. Plasma Model
The gas/plasma tube is a highly nonlinear load, presenting a very high impedance as a gas or a very low impedance as a plasma (with negative incremental impedance).The accurate simulation of the double pulse generator requires a load with a dynamic nonlinear behavior similar to plasma.There are several examples of mathematical models to describe plasma's electric and/or physical behavior.Cassie's arc model (17) considers the arc temperature, the current density, and the electric field to be constant, with the arc's cross section varying with current and time, and the energy being lost through thermal convection.This model was chosen for these simulations because it is considered the most suitable for high currents [29].The Cassie arc model can be described by the differential equation, where R represents the plasma's (time-variable) resistance, θ is the arc time constant (the ratio between energy stored per unit volume and the energy loss per unit volume), V is the tube applied voltage, and V 0 is the plasma voltage in steady state Equation ( 17) is modeled in a PSpice schematic, which performs the computations using the applied voltage (V ) as the main variable.In Figs. 3 and 4, the plasma impedance is presented.When subjected to the ignition pulse the impedance falls sharply.

B. Simulations of the Double Pulse Generator
The double pulse generator circuit was implemented in the PSpice environment, using the plasma model as the load (with Fig. 4. Voltage and impedance as a function of time for a simulation of the double pulse generator circuit waveforms, where Z tube is the load impedance, V isw is the voltage on the ignition switch, V Sh is the voltage on the heater switch, V isn is the voltage on the ignition snubber, V hsn is the voltage on the heater snubber, V Di is the voltage on the ignition diode, V Dc is the voltage on the coupling diode, and V tube is the voltage in the plasma tube; the transition through the six regimes of operation (steps) is represented by the dashed lines.
the load impendace represented by the Z tube waveform).The first waveforms to analyze (Fig. 3) are the currents at the ignition switch I sw , at the ignition snubber I sn , and at the plasma tube I tube (probes from Fig. 1), following the same steps as described in Fig. 2.
The current in the primary winding rises during the switchtextscon state (Step 2), storing magnetic energy in the transformer.When the switch turns off (at primary peak current), the snubber is activated clamping the voltage at the switch.After the plasma ignition, the tube's impedance is reduced, and the current stabilizes (Step 4).The tube current rises again after the heater switch turns on (Step 5).Ideally, it would form a perfect square pulse, but due to the parasitic impedances in the load, the current rise is not instantaneous.The heating system allows the tube to reach a higher current with a smaller voltage (when compared with the ignition voltage), reflecting the previous reduction of the tube's impedance by the ignition system.Since the plasma remains conductive after the heating event, on the sixth step, the current falls slowly as the transformer's remaining magnetic energy dissipates.
In Fig. 4, the voltages at the ignition switch V isw , heater switch V Sh , snubber V isn , tube V tube , ignition diode V Di , and the coupling diode V Dc are displayed.In the third step, the snubber voltage is multiplied by the transformer ratio on the secondary (tube voltage).As the plasma ignition occurs (Step 4), the tube voltage drops, as the plasma becomes conductive.We can see that the ignition switch S ign initially has a voltage equal to the ignition source voltage (V ign = 2 kV), falls sharply to zero as the switch turns on, and rises again with the switching off (with an initial spike, caused by the transformer's inductance).The ignition diode voltage V Di rises during the switch-ON period, up to the value of the input voltage times the transformer ratio.The coupling diode D c holds off the tube voltage during the third step.The heater switch works as predicted, holding off the heater source voltage (V h = 8.5 kV) and the spike caused by the plasma ignition (in Step 4) until it turns on in Step 5.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

IV. EXPERIMENTAL RESULTS
The operation of both subcircuits and the full double pulse generator was tested with the plasma generation within different discharge tubes, using low-pressure Ar.The test tubes had lengths of 1.6 and 5 m, an inner diameter of 25 mm, a circular anode on one end, and a pin cathode on the other.The return cage consists of four wires and has an ignition gap of 35 cm near the cathode, as described in Section I-A.

A. Heater Circuit
The heater circuit, operating without ignition, was tested using a 1.6-m tube, with 25-mm inner diameter, and filled with Ar at 2 Pa (close to the minimum in Ar Paschen curve).Larger lengths and pressures would make the plasma ignition impossible with just the heater pulse voltage.From the plot in Fig. 5, a delay (between the heater switch turn-on and the beginning of the pulse) was measured to be over 8.66 µs and the pulse's jitter measured around 1.29 µs.The jitter and the delay measured, even at lower lengths, are not compatible with the application requirements [12], justifying the use of the higher voltage ignition pulse.

B. Ignition Circuit
For the ignition circuit tests, the circuit presented was assembled (Fig. 6) to match the parameters in Table II.The experiments were performed using a 5-m tube filled with Ar at 10 Pa.The ignition circuit uses the same current sensor locations as in Section III-B and Fig. 1.
1) Breakdown Voltage Test: A relevant parameter to measure is the breakdown voltage of the plasma.After the switch-OFF, when the snubber diode is activated (Step 3), there is a delay between the primary switch-OFF and the plasma ignition.Consequently, the plasma current is zero until the ignition occurs.This means that before the ignition, the current measured in the secondary flows through the resistor parallel to the tube R ptube .Because R ptube is known, it is possible to approximately calculate the value of the breakdown voltage from the measured secondary current right before the ignition.
The moment of the ignition can be detected in Fig. 7 (vertical line in Step 3) by a fast spike of current on the secondary, followed shortly afterward by a drop in snubber current.For this shot, the tube current before ignition was I ign0 ≈ 1.53 A and the breakdown voltage is estimated to be V br ≈ 15.3 kV, given that the parallel resistance for this test was R ptube = 10 k .Tests at different input voltages suggest an ignition voltage interval between 15 and 24 kV, for 10-Pa Ar.The plasma ignites before the tube voltage reaches 120 kV that the ignition circuit was designed to apply, and this can be due to the difference in plasma geometries from [16] (especially the presence of the 35-cm gap).The higher voltage potential is, however, still important to charge fast the parasitic components of the tube, leading to the desired nanosecond jitter.
2) Ignition Jitter Test: In order to have high reproducibility, the jitter is a main concern in this project, and its minimization is one of the main purposes of the ignition circuit.
From the plot in Fig. 8, the jitter measured was approximately 55 ns, by comparing the ignition time of 100 shots.This jitter corresponds to approximately 5% of the typical delay between the ignition switch turn-off and the beginning of the ignition pulse (1 µs), allowing to set the trigger for the heater pulse comfortably with a stable ignition current.

C. Double Pulse Generator
When using both pulses, after the ignition event, the tube's impedance drops significantly.It is possible then to increase  The main objective of the double pulse generator is the reproducibility of the high current discharge.Therefore, to test the reproducibility of the circuits, the experiment was repeated for 100 discharges [Fig.9(b)], with the same parameters.
A jitter of 12 ns for the rising edge of the heater pulse was measured also using the superposition of 100 shots.This jitter corresponds to approximately 0.1% of the heater pulse duration, and therefore, we expect the impact of the heater jitter on the plasma reproducibility to be close to this 0.1% fraction.On the other hand, there is a significantly higher (3%) variability in the heater current amplitude.This variability can be caused by many factors, including the change in the gas pressure and composition over the 100 discharges.
The difference in the jitter results with and without (Section IV-A) the ignition pulse justifies the use of the double pulse configuration.

V. CONCLUSION
This article describes the development of a double pulse generator for a plasma source to be used for wakefield acceleration applications.The design, simulation, and experimental characterization of the electrical modules were presented in detail.
The double pulse generator uses two circuits (ignition and heating) to optimize performance and reduce power.The ignition circuit has a transformer inductive discharge topology and uses a solid-state fast switch stack assembly, able to generate over 100 kV.The heating circuit is a capacitive discharge pulse generator, able to raise the current over 400 A, after ignition.Both circuits are independently connected to the plasma tube through coupling diode stacks.
The performed experiments show that the circuit with the double pulse topology is able to ignite a plasma arc in test tubes up to 5 m long with the required reliability (12-ns jitter-Table I).Also, after ignition, these arcs can lead to a high current value (above 300 A) by a lower voltage capacitive discharge.
The simulations using a plasma model were validated, sharing similar results to the ones obtained experimentally justifying its employment on future developments.
Future work will aim to measure the reproducibility of the plasma properties and to isolate the origin of the current variations detected in the heater pulse.Furthermore, the scalability of these long plasmas from tens to hundreds of meters will require the connection in series of tens of these plasma tubes using alternate common cathodes and anodes, requiring accurate current balancing.

Fig. 1 .
Fig. 1.Main power circuit of the double pulse generator and the plasma load.

Fig. 3 .
Fig. 3. Current and impedance as a function of time for a simulation of the double pulse generator circuit waveforms, where Z tube is the load impedance, I sw is the current in the ignition switch, I sn is the current in the ignition snubber, and I tube is the current in the plasma tube; the transition through the six regimes of operation (steps) is represented by the dashed lines.

Fig. 5 .
Fig. 5. Current as a function of time for the heater circuit jitter test-100 discharges overlapped (V h = 7 kV, p = 2 Pa, and 1.6-m tube length).

Fig. 7 .
Fig. 7. Currents as a function of time for the ignition circuit breakdown voltage test, where I sw is the current in the ignition switch, I sn is the current in the ignition snubber, and I tube is the current in the plasma tube-100 discharges overlapped (V ign = 2 kV, p = 10 Pa, and 5-m tube length).

Fig. 8 .
Fig. 8. Currents as a function of time for the ignition circuit jitter test, where I sw is the current in the ignition switch, I sn is the current in the ignition snubber, and I tube is the current in the plasma tube (V ign = 3.2 kV, p = 10 Pa, and 5-m tube length).

Fig. 9 .
Fig. 9. Currents as a function of time for the double pulse generator circuit, where I sw is the current in the ignition switch, I sn is the current in the ignition snubber, and I tube is the current in the plasma tube (V ign = 2 kV, V h = 8.5 kV, p = 10 Pa, and 5-m tube length).(a) Single discharge, the transition through the six regimes of operation (steps) is represented by the dashed lines.(b) Jitter measurement with 100 discharges overlapped.