Excess emission has been observed from velvet cathodes with total emission times >150 ns. In this diode experiment, we produce a sub-relativistic electron beam with the ability to consistently change γ from 1.2 to 1.5 and β = 0.5–0.75. Electron emission in this particular diode geometry requires electric fields >40 kV/cm. The current increases at steady rates >0.05 A/ns after the head of the pulse, indicating an expansion of the emission surface and reduction in the effective AK gap. Small transients of excess emission (or arcs) are consistently observed for current pulses exceeding 150 ns. The excess emission results in beam loaded levels 10 kV on the diode voltage. The effects described here are compounded as diode voltage is increased. The principal objective of these experiments is to quantify electric field emission thresholds, current ramps, excess emission delays, effective beam loading, and impedance collapse.

The use of velvet fabric as a high current density ( J > 10 A / cm 2) cathode source was initiated by Adler and Gilgenbach nearly 40 years ago.1,2 Almost immediately afterward this type of cathode was incorporated into the ATA3,4 and FXR injectors5,6 at LLNL. It was also studied thoroughly in the relativistic electron beam experiment (REX) or the DARHT Axis-1 injector test stand.7 Since this time, these cathodes have been a trusted source for emitters in linear induction accelerators with single pulses <100 ns throughout the world.8–11 

The use of velvet emitters for multiple pulse injectors and accelerators has also been explored at ATA,3,4 FXR,5,6 Ref. 12, and MI-2.13 Research on MI-213 indicated a linear increase in current on the second pulse of up to 20% for interpulse spacings >500 ns. PIC modeling utilizing the LSP code and space charge limited emission estimate the emission surface expands up to 800  μm for interpulse spacings of 3  μs.

A test stand has recently been developed to test candidate cathodes for intense electron accelerators with addressable voltage pulse lengths of 0.3–2.2  μs. The pulse lengths provided by this test stand are most optimal for emitters with low electric field thresholds (<100 kV/cm). The test stand is suitable to study both field emission cathodes and photocathodes. Initially, we are characterizing the temporal evolution of the current and the resulting extracted beam from a velvet emitter.

The results presented indicate the cathode plasma expands and the extracted current increases at a relatively consistent rate for the first 150 ns of the current pulse. As will be shown below, this growth rate or expansion velocity is dependent on the diode voltage. Transients in the current pulse are observed after this steady slope in current. Results indicate there is a charge threshold or surface charge density threshold of 8  μ C / cm 2 above which these transients begin to persist.

Previous experiments noted a 60% increase in gun perveance over a 300 ns pulse for current densities 50 A / cm 2.14 Reference 15 observed nearly 3 × increase in gun perveance for lower current densities over a 1.5  μs pulse duration. No abrupt transients were observed in either case. Some of this increase in perveance seen by previous authors14,15 is associated with a fall in the voltage pulse while the current continues to persist. This is the first experimental assessment of excess emission thresholds from a velvet emitter. We have also assessed beam loading and impedance collapse, which is correlated with the excess electron emission. These measurements indicate this type of cathode is not suitable for pulse lengths >150 ns or a surface charge density of >8  μ C / cm 2. However, it may meet performance requirements with two short, t < 50 ns, pulses with minimal interpulse reflections.

The diode was designed for these long pulse, low- β electron experiments utilizing the TRAK16,17 electron-gun design code. The diode was constructed with a 22 mm AK gap, a 25 mm-diameter emitter, and recessed 3 mm behind the edge of the cathode shroud. An example model of the diode with a voltage of 250 kV produces a maximum E-field on the most downstream edge of the cathode shroud of 140 kV/cm (Fig. 1). This provides an average electric field of 73 kV/cm on the emitter surface without emission. Diode voltages near 300 kV are applied with this AK gap, but are susceptible to diode breakdown with pulse lengths near 500 ns. The calculated electron current from the 25 mm- ϕ emitter is 144 A at 250 kV. This is calculated utilizing the two-dimensional TRAK code, which includes local fields in the diode and calculates the space-charge-limited emission off the recessed emitter surface assuming no expansion. The code includes the beam self-fields and the resulting space charge depression on the cathode face. As will be explained below, there is a slight increase in the initial measured current.

FIG. 1.

TRAK model of the diode geometry zoomed into the diode region showing the (a) absolute electric field levels and (b) cathode emission and beam transport for the first few cm.

FIG. 1.

TRAK model of the diode geometry zoomed into the diode region showing the (a) absolute electric field levels and (b) cathode emission and beam transport for the first few cm.

Close modal

The experimental configuration used to characterize cathodes is shown in Fig. 2. The diode and insulator were designed to hold off fields <200 kV/cm for pulses up to 2.2  μs. A 20  Ω, 4-stage, pulse-forming network (PFN) Marx18–20 provides a nominal 300 kV, 2.2  μs-long pulse to the cathode shroud. More specifically, the voltage pulse has a 90 ns-long rise time from 10% to 90% amplitude as shown in Fig. 3. The voltage reaches its peak amplitude at 150 ns with a 15% overshoot. This ramps down to 300 ns before having a slow linear increase thereafter. The length of the voltage pulse is controlled by a spark gap triggered crowbar.

FIG. 2.

(a) Elevation view of the cathode test stand starting from the left with the compensation (Comp.) can, diode, and associated diagnostics pointed out. The 2.2 cm AK gap is shown for reference. (b) The top cross-sectional view indicates two imaging cameras for: the cathode face (red) and current density imaging diagnostics (orange); locations of several diamond radiation detectors (DRDs) are pointed out as well. The lines of sight and sample data sets are also shown.

FIG. 2.

(a) Elevation view of the cathode test stand starting from the left with the compensation (Comp.) can, diode, and associated diagnostics pointed out. The 2.2 cm AK gap is shown for reference. (b) The top cross-sectional view indicates two imaging cameras for: the cathode face (red) and current density imaging diagnostics (orange); locations of several diamond radiation detectors (DRDs) are pointed out as well. The lines of sight and sample data sets are also shown.

Close modal
FIG. 3.

Top row: measurements at maximum diode voltages of 220 and 255 kV with a 25 mm-diameter cathode. Bottom row: measurements at maximum diode voltages of 180, 200, 220, 235, and 255 kV with a 15 mm-diameter cathode. (a) Measured diode voltages; (b) measured diode voltages zoomed in to show the 15% overshoot and flatter portion of the pulse; (c) the extracted electron current. The associated legend, indicating the shot number and PFN charge voltage, for each row is shown in the first panel.

FIG. 3.

Top row: measurements at maximum diode voltages of 220 and 255 kV with a 25 mm-diameter cathode. Bottom row: measurements at maximum diode voltages of 180, 200, 220, 235, and 255 kV with a 15 mm-diameter cathode. (a) Measured diode voltages; (b) measured diode voltages zoomed in to show the 15% overshoot and flatter portion of the pulse; (c) the extracted electron current. The associated legend, indicating the shot number and PFN charge voltage, for each row is shown in the first panel.

Close modal

Voltage is monitored in two locations with capacitive pickups or E-dots. These monitor the differential voltage on a local electrode. One measurement is made from an electrode electrically connected to the cathode stalk and ballast resistor inside the oil filled compensation (Comp.) can (Fig. 2). The second measurement is made inside the vacuum aligned axially with the upstream edge of the cathode shroud. The measurements agree well to within 2% when there is no emission. Each measurement is numerically integrated to obtain the diode voltage. Each E-dot was calibrated over a range of voltages with a known load.

The current extracted from the 25 mm- ϕ cathode is 160 A near the head, for a maximum diode voltage of 255 kV, and this increases linearly to 194 A over the next 120 ns [Fig. 3(c)]. The current is monitored with an array of differential B-dots21 or a Beam Position Monitor (BPM) (Fig. 2). The BPM array is situated at an axial location of 12.3 cm. The beam is generally terminated by the scintillator or current density diagnostic shown in Fig. 2(a) at an axial distance of 14–16 cm depending on the experimental setup.

An array of diamond radiation detectors (DRDs) were used to help characterize the diode dynamics, more specifically the scattered and excess electrons. Traditionally, DRDs have been used for soft x-ray detection22–24 and more recently for beta detection in a similar energy range.25,26 The first were setup in the diode through an angular port [Fig. 2(b)]. A second set was deployed in the same axial location as the BPM array. The final set was deployed downstream of the current density diagnostic. We performed both K-edge filtering and electron ranging measurements with the DRDs to determine whether the signals were dominated by scattered electrons.

Two separate image intensified fast gated charge-coupled devices (ICCDs),27 mounted external to the cathode vacuum vessel, are used to characterize the cathode emission and beam current density. The camera shown in the top of Fig. 2(b) (shaded in red) is mounted at a 33 ° angle to the propagation axis of the beam and is used with a mirror and the mirrored face of the anode to view the light on the cathode face. The images from this camera are used to verify the charge density of the emitter as discussed below and in Ref. 10. The camera shown in the bottom of Fig. 2(b) (shaded in orange) is mounted parallel to the propagation axis of the beam and is used with a set of turning mirrors to either view the beam induced Cherenkov or the subsequent x-ray radiation induced scintillation. The current density measurements made at this electron energy range are sensitive to a series of physical phenomena which are material dependent. These include electron scatter, x-ray scatter, Cherenkov thresholds, and total internal reflection; each of which is dependent on the material thickness and dielectric properties.28,29 Details of these current density measurements will be included in a future publication.

The emission process from our rayon velvet fibers and the generation of an electron beam is described in detail in Refs. 10, 30, and 31. Based on measurements and calculations from previous authors, the surface discharge on the velvet produces electron densities < 10 15 cm 3.10,14 Only a small fraction of the electrons (<0.1%) are extracted from the sheath of this surface plasma and accelerated across the 2.2 cm gap. This particular diode geometry requires a minimum electric field of 46 kV/cm to observe current extracted through the diode for the 15 mm-diameter cathode and 64 kV/cm for the 25 mm-diameter cathode. The differences are due to the different radial edges of the velvet and the field depression. The 15 mm cathode has an exposed triple point. The measured voltages and currents for the two different cathode sizes are shown in Fig. 3.

The panels on the top row are two representative shots with the 25 mm-diameter cathode with the mean emission voltages of 219 and 258 kV. The measurements with this larger cathode exhibit signs of a slope in the current and excess emission at later times in the pulse. These details will be explained in Sec. IV below. Emission is not observed with this size cathode until a minimum voltage of 214 kV is reached or an E-field of 63.2 kV/cm. The emission delay is 115.0 ± 7.5 ns relative to the start of the voltage pulse [Fig. 4(a)]. The start of the voltage pulse is defined as time at which the voltage is 10% of the maximum and the start of emission is defined as 10% of the head current. An increase in the diode voltage only slightly reduces the emission delay to 104.0 ± 4.5 ns. As will be shown below, this larger cathode has turn on delays that agree with lower voltage operations of the smaller cathode. However, there is less statistical variance in the emission delay of this larger cathode as shown in Fig. 4(b).

FIG. 4.

(a) Emission delay vs charge voltage. (b) Emission delay vs the actual emission voltage and the electric field threshold. All data shown here are from a larger group of shots, including the subset shown in Fig. 3.

FIG. 4.

(a) Emission delay vs charge voltage. (b) Emission delay vs the actual emission voltage and the electric field threshold. All data shown here are from a larger group of shots, including the subset shown in Fig. 3.

Close modal

Measurements with a 15 mm-diameter cathode are shown in the bottom panels of Fig. 3. Peak voltages reached up to 275 kV in these experiments however, emission from the cathode (velvet tufts) begins much sooner. The lowest voltage at which we observed emission was 144 kV, which corresponds to an E-field on the surface of the velvet of 42.5 kV/cm. There is a large statistical variation in the emission delay for these data as indicated through the error bars in Fig. 4(b). Emission at the lowest operating voltage has a corresponding delay of 133.9 ± 23.2 ns relative to the voltage pulse. As the voltage is increased, we observed a monotonic decrease in the average emission delay from >130 ns down to <70 ns as indicated in Fig. 4(a). This is expected because the time to reach the necessary field for emission is decreased. The emission voltage ranges from 144 to 215 kV, with more statistical variance at the middle charge voltages [Fig. 4(b)]. This statistical variance is shown with the error bars in all panels in Fig. 4, which are largest at charge voltages of 60 and 65 kV. Some of the statistical variance in the emission delay and voltage is due to the 90 ns rise time in the voltage pulse. The mean emission voltage for all shots with the 15 mm cathode is 179 kV. The corresponding E-fields on the cathode face range from 46.3 ± 0.7 to as high as 56.3 ± 7.2 kV/cm [Fig. 4(b)].

The current profiles shown in Fig. 3 indicate the appearance of a steadily increasing slope after the head of the pulse for t < 350 ns. Due to the relatively slow rise time ( 90 ns) of the voltage pulse, there is some statistical variance in the turn on and rise time of the emission for the smaller cathode as shown in Fig. 4(a).

A larger group of shots, including the subset shown in Fig. 3, were examined over the full operating range of voltages to determine the mean slope in the current after the head of the pulse [Fig. 5(a)]. The data examined for the 25 mm-diameter cathode indicate the current slope is just above 0.3 A/ns for a maximum diode voltage of 220 kV; this is slightly reduced for a peak diode voltage of 255 kV. The data examined for the smaller cathode indicate the current slope is <0.1 A/ns for voltages 200 kV. Then, it slightly increases to 0.15 A/ns for voltage ranges between 218 and 255 kV. The maximum exceeds 0.25 A/ns at peak operating voltages of 275 kV.

FIG. 5.

(a) Current slope for the 25 and 15 mm-diameter cathodes at t < 350 ns. The calculated AK gap and resulting expansion velocity from the current slope for the (b) 25 mm-diameter cathode and (c) 15 mm-diameter cathode. (d) The measured current at the head of the pulse for a 25 mm-diameter cathode on shot 6277 (blue) in comparison to the calculated current for the diode as built without expansion (TRAK_1, red dots) vs the calculated current by including the necessary expansion for the corresponding diode voltage (TRAK_2, black squares). The TRAK_2 data correspond to an expansion of the emission surface of 10 mm/ μs.

FIG. 5.

(a) Current slope for the 25 and 15 mm-diameter cathodes at t < 350 ns. The calculated AK gap and resulting expansion velocity from the current slope for the (b) 25 mm-diameter cathode and (c) 15 mm-diameter cathode. (d) The measured current at the head of the pulse for a 25 mm-diameter cathode on shot 6277 (blue) in comparison to the calculated current for the diode as built without expansion (TRAK_1, red dots) vs the calculated current by including the necessary expansion for the corresponding diode voltage (TRAK_2, black squares). The TRAK_2 data correspond to an expansion of the emission surface of 10 mm/ μs.

Close modal

These particular dI/dt in Fig. 5(a) are used to evaluate the reduction in the AK gap using the 1D Child-Langmuir Law32,33 at each operating voltage range for both the 25 and 15 mm-diameter cathodes [Figs. 5(b) and 5(c)]. The AK gap is only slightly reduced for the 25 mm-diameter cathode; the expansion velocity at the lower operating voltage is large because of the large dI/dt. The expansion velocity for the 255 kV case is 18 mm/ μs using this method. When examining the 15 mm-diameter cathode, for all cases the AK gap is reduced to <18 mm from the original 22 mm. The AK gap does not decrease in a perfect linear relationship to the voltage, but there is a downward trend. The highest operating voltage indicates the AK gap is reduced to <15.5 mm. The dI/dt and reduced AK gap over the time interval evaluated corresponds to a gap closure velocity. The lowest operating voltages V 180 kV indicate the plasma expands at a rate of 9 mm/ μs. There is an increasing trend in the plasma expansion velocity, reaching a maximum >16 mm/ μs at 275 kV.

The measured current at the head of the pulse for a 25 mm-diameter cathode is examined more closely for peak diode voltage of 255 kV on shot 6277 vs what is calculated with TRAK.16,17 The measured current, shown in blue in Fig. 5(d), indicates the current increases at a linear rate of 0.29 A/ns in the first 120 ns. The voltage [Fig. 3(b)] used to extract the beam steadily drops 15% from 150 to 300 ns, so the expected current should drop proportional to the diode perveance. This expected drop in current is shown with the calculated points in red (TRAK_1). In order to calculate the same measured current, the emission surface must expand inside the assembled 3 mm recess. The expansion rate is small initially, 0.5 mm, but the recess is reduced by 1.7 mm to an effective recess of 1.3 mm at 300 ns. So the cathode plasma has expanded at a rate of 10 mm/ μs. Note the differences in the calculated velocities between Figs. 5(b) and 5(d). TRAK utilizes the actual diode geometry and models the two-dimensional particle transport, and the calculation in Fig. 5(b) estimates a change in the AK gap and resulting velocity from the 1D Child-Langmuir Law; the later has more error.

Aside from a steadily increasing dI/dt, we observe transients in the current pulse [Fig. 3(c)], which we describe as excess emission and may be an arc due to accumulated charge on the cathode. We have analyzed the statistical delay of these first excess emission points from the same data set examined in Figs. 3–5. The excess emission is at least 30% higher than the current at the head of the pulse for all shots examined. The early transients are generally 50% of the peak amplitude of the maximum current observed in these 500 ns-long current pulses, meaning they generally increase in intensity as the pulse increases. The intensity of these transients and their spacing is shot dependent. Through our operational range, we consistently observe excess emission at every voltage level for both cathode sizes. The trend that we observe is a temporal delay in the excess emission as seen in Fig. 6. This excess emission delay (EE delay) is referenced to the beginning of the current pulse. At our lowest operating voltage for the 15 mm-diameter cathode, 160 kV, the delay in excess emission is at least 200 ns into the current pulse, which corresponds to a charge threshold just under 10  μC. We believe there is a charge density limit for this particular velvet. Once this temporal limit is reached, emission becomes catastrophic and unstable. Velvet is a dielectric, so once a surface charge limit is reached it must dissipate and it begins to arc. This explanation seems logical because this charge limit increases proportionally to the voltage. As the diode voltage is increased, the excess emission delay [EE Delay, Fig. 6(a)] is reduced to <160 ns for the peak operating voltage for the 15 mm-diameter cathode. The 25 mm-diameter cathode has an excess emission delay that is 30 ns longer at the 220 kV voltage level, but the statistical variance of the two cathodes overlap at this level. The delays agree well for both cathode sizes at 255 kV.

FIG. 6.

(a) The relevant excess emission delay (EE Delay) for each operating voltage is shown in addition to the (b) measured charge threshold and (c) charge density threshold prior to the excess emission. All data shown here are from the same data set examined in Figs. 35.

FIG. 6.

(a) The relevant excess emission delay (EE Delay) for each operating voltage is shown in addition to the (b) measured charge threshold and (c) charge density threshold prior to the excess emission. All data shown here are from the same data set examined in Figs. 35.

Close modal

One thing to note is the statistical variance in the error level of the excess emission delay at each voltage. This points to the stochastic nature of the excess emission. Voltage ranges 200 kV and a total charge in excess of 10  μC is guaranteed to lead to excess emission for a 15 mm-diameter velvet cathode. This limit is above 20  μC for the 25 mm-diameter cathode. These cathodes generally only emit from 80% of the surface so once the surface charge density exceeds 8  μ C / cm 2, this particular velvet becomes vulnerable to stochastic excess emission; Fig. 6(c) corroborates this. The data for both cathodes indicate a minimum surface charge density near 8  μ C / cm 2 for the low voltage operating points; error bars indicate lower values in some cases. When considering the use of a velvet cathode for a diode design, the charge density limit ( μ C / cm 2) must be considered.

When examining the voltage supplied to the cathode and current extracted from the diode it is evident, as explained above, there is excess emission when the current pulse length is >150 ns (Figs. 3 and 6). Another point that may seem subtle is the beam loading on the PFN voltage. Beam loading is commonly observed in induction linacs34 when a high current electron beam loads down the voltage in an induction cell. There is a transformer coupling between the induction cell and the beam; the beam creates a load impedance on the cell reducing the effective energy that can be added to the beam. While there is no transformer coupling in the diode here, high enough beam current or a diode breakdown can load down the voltage from the PFN.

Figure 7(a) shows the individual diode voltage and extracted current waveforms overlaid, for example, shot 7609 with the 15 mm-diameter cathode. The PFN was charged to 75 kV, which correlates to a maximum diode voltage of 276 kV on this particular shot. The current begins to rise at 100 ns for this shot and a current ramp of 0.28 A/ns begins after the rise. Two to three small transients of excess emission are observed at t >230 ns. Several notable transients of excess emission appear at 342, 548, and 600 ns. A dip is shown in the diode voltage just before each of these times. The current lags the voltage by 10 ns, which is the amount of time it takes the PFN to charge up the current path, similar to an inductive circuit.

FIG. 7.

Example shot 7609 displaying (a) PFN voltage (blue), extracted current (red), and the scattered electron flux in the diode (DRD01, orange) for a 15 mm-diameter cathode. (b) The resulting diode impedance (red) indicates a gradual collapse with the current slope and transients with excess emission. The gun perveance (black) and the scattered electron flux downstream of the diode (DRD02, green) are overlaid as well. (c) Three axially displaced DRDs are shown for comparison, indicating the difference in scattered electron signal in the diode (DRD01, orange), directly downstream of the diode (DRD02, green), and downstream of the current density diagnostic (DRD03, purple). (d) The unloaded open circuit voltage (black) and loaded (blue) voltage waveforms. (e) Calculated beam loaded voltage difference ( ΔV) for t > 300 ns subtracting the difference between the two waveforms in (d, red) and utilizing a fit from the unloaded open circuit voltage (orange) (note time scale differences).

FIG. 7.

Example shot 7609 displaying (a) PFN voltage (blue), extracted current (red), and the scattered electron flux in the diode (DRD01, orange) for a 15 mm-diameter cathode. (b) The resulting diode impedance (red) indicates a gradual collapse with the current slope and transients with excess emission. The gun perveance (black) and the scattered electron flux downstream of the diode (DRD02, green) are overlaid as well. (c) Three axially displaced DRDs are shown for comparison, indicating the difference in scattered electron signal in the diode (DRD01, orange), directly downstream of the diode (DRD02, green), and downstream of the current density diagnostic (DRD03, purple). (d) The unloaded open circuit voltage (black) and loaded (blue) voltage waveforms. (e) Calculated beam loaded voltage difference ( ΔV) for t > 300 ns subtracting the difference between the two waveforms in (d, red) and utilizing a fit from the unloaded open circuit voltage (orange) (note time scale differences).

Close modal

The excess current and loaded voltage combine as an effective impedance collapse [Fig. 7(b)]. Impedance collapse has been measured in high current diodes.35 Reference 35 indicated a steady collapse with several different materials and current densities > 200 A / cm 2. Utilizing formulation shown in Refs. 9 and 35, we calculate Z(t) and the time dependent gun perveance. Recall the voltage is 15% higher 150 ns prior to the minimum which is reached at 300 ns. The steady ramp in the current over this same time frame compounds the reduction in Z from 2.5 to 1.5 k Ω. Later in the pulse excess current leads to impedance collapse to <800  Ω and 2 × increase in gun perveance. Each transient in the current [Fig. 7(a)] maps to the fluctuation in gun perveance we observe in Fig. 7(b).

The scattered electron flux, or excess current, in the diode (DRD01) is also overlaid with the current and voltage in Fig. 7(a). This measurement is provided by a 2 × 3 mm 2 diamond collector.36 DRD01 indicates identical transients in the diode as the average beam current measured downstream. Nearly 50% of the electron flux is collected from the transient at 600 ns indicating most of the electron current is transported through the diode outside of this time. Two additional scattered electron measurements are made after the electrons are extracted through the diode. The first is measured in the BPM array, at an axial distance of 12.3 cm (DRD02) just upstream of the current density diagnostic; this is overlaid with the impedance and gun perveance in Fig. 7(b). The final scattered electron measurement is made at roughly 21 cm (DRD04). As expected, the scattered electron signal is highest on the upstream side of the current density diagnostic, where the electron beam is terminated. Electrons were ranged out by a 200  μm-thick Cu foil in this shot series.37–40 The subsequent beam induced radiation pattern is measured with a 150  μm-thick BC-400 scintillator directly downstream. The scattered radiation measurement downstream of the current density diagnostic (DRD04) is severely attenuated as expected. The three DRDs are overlaid for comparison in Fig. 7(c).

A comparison of the loaded voltage (blue) is shown vs the open circuit voltage (black) in Fig. 7(d). The open circuit voltage is obtained from an identical operating point when no emission is achieved in the diode. A clear “loading” of the diode voltage is shown and this is significant compared to normal shot-to-shot variations of 1 - σ = ± 2 kV. After processing, we see nearly identical transients in the loaded voltage in comparison to the current, impedance, and perveance waveforms; the last three just lag due to the inherent inductance in the circuit.

We also perform a linear fit to the open circuit voltage after the minimum at 300 ns, which is V ( kV ) = 222.7 0.039t. As an additional assessment, we calculate the exact beam loaded voltage by subtracting the measured diode voltage from the open circuit voltage slope in Fig. 7(e). This voltage difference is calculated in two manners, the first is a simple waveform subtraction (red) and the second is a subtraction from the linear fit just mentioned (orange). It is shown that they agree well except for the natural frequency fluctuations not accounted for in the fit. This particular shot indicates the loaded voltage reaches a peak >20 kV, which is 10% of the supplied voltage at this time frame.

We have measured emission limitations from a rayon velvet fiber cathode when the current pulse exceeds 150 ns. The observed electric field threshold for this diode geometry exceeds 40 kV/cm, but this depends on both the operating voltage and the cathode size. The slow, 90 ns rise time of the voltage pulse leads to emission delays >60 ns relative to the start of the voltage pulse; this is also dependent on the operating voltage and cathode size.

Measurements indicate there is a slope in the current profile for both cathode sizes. This dI/dt over the first 120–150 ns of emission is voltage dependent for this diode geometry, but it exceeds 0.05 A/ns for the 15 mm-diameter cathode and is close to 0.3 A/ns for the 25 mm-diameter cathode. These current slopes indicate expansions of the emission surface with velocities >9 mm/ μs. Exact expansion must be modeled with a 2D diode code. After the cathode plasma has expanded in the first 150 ns, we begin to observe excess emission. Lower voltages tend to have a longer delay prior to excess emission due to a lower level of initial charge. Both cathodes indicate a surface charge density >8  μ C / cm 2 is required to observe these effects. This excess emission leads to effective beam loading and impedance collapse as well. Loaded voltages in excess of 10 kV are common and in some cases higher. Diode impedance easily collapses to <1 k Ω.

The results presented provide the first experimental assessment of excess emission thresholds for a velvet emitter. We continue to expand our diagnostic suite which includes thermal cathode imaging and optimum current density measurements including both Cherenkov emitters and indirect x-ray scintillation. We plan to use similar techniques to diagnose other candidate cathode materials.

This work was supported by the National Nuclear Security Administration of the U.S. Department of Energy under Contract No. 89233218CNA000001. We would like to take the opportunity to thank Don Roeder, Ross Roybal, Damien Frenzel, Anthony Chavez, Sharon Dominguez, and Gabriel Ortiz for their manufacturing and design support. We would also like to thank James Maslow for his infrastructure support.

The authors have no conflicts to disclose.

J. E. Coleman: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Resources (lead); Supervision (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). M. R. Howard: Data curation (supporting); Formal analysis (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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