Search NASA⌕ Search

SEARCH · Search NASA

Results for “discharge current”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16

Special Test Methods for Batteries

Various methods are described for measuring heat generation in primary and secondary batteries as well as the specific heat of batteries and cell thermal conductance. Problems associated with determining heat generation in large batteries are examined. Special attention is given to monitoring temperature gradients in nickel cadmium cells, the use of auxiliary electrodes for conducting tests on battery charge control, evaluating the linear sweep of current from charge to discharge, and determining zero current voltage. The fast transient behavior of batteries in the microsecond range, and the electrical conductance of nickel sinters in the thickness direction are also considered. Mechanical problems experienced in the vibration of Ni-Cd batteries and tests to simulate cyclic fatigue of the steel table connecting the plates to the comb are considered. Methods of defining the distribution of forces when cells are compressed during battery packaging are also explored.

Gross, S.↗

Eagle-Picher SPV development

The topics covered are presented in viewgraph form and include the following: Eagle-Picher heritage - single pressure vessel (SPV) technology; SPV units in process at Eagle-Pitcher; design features; basic battery design features; cell development considerations; SPV boiler plate cell; cell development activity; SPV cell capacity test - charge and discharge; and current plans.

Brill, Jack↗

EOS-AM1 Nickel Hydrogen Cell Interim Life Test Report

This paper reports the interim results of the Earth Observing System AM-1 project (EOS-AM-1) nickel hydrogen cell life test being conducted under contract to National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) at the Lockheed Martin Missiles and Space (LMMS) facility in East Windsor, NJ; and at COMSAT Labs., Clarksburg, MD. The purpose of the tests is to verify that the EOS-AM-l cell design can meet five years of real-time Low Earth Orbit (LEO) cycling. The tests include both real-time LEO and accelerated stress tests. At LMMS, the first real-time LEO simulated 99 minute orbital cycle started on February 7, 1994 and the test has been running continuously since that time, with 13000 LEO cycles completed as of September 2, 1996. Each cycle consists of a 64 minute charge (VT at 1.507 volts per cell, 1.06 C/D ratio, followed by 0.6 ampere trickle charge) and a 35 minute constant power discharge at 177 watts (22.5% DOD). At COMSAT, the accelerated stress test consists of 90 minute orbital cycles at 60% DOD with a 30 minute discharge at 60 amperes and a 60 minute charge at 40 ampercs (VT at 1.54 volts per cell to 1.09 C/D ratio, followed by 0.6 ampere trickle charge). The real-time LEO life test battery consists of seven, 50AH (nameplate rating) Eagle-Picher, Inc. (EPI) Mantech cells manufactured into three, 3-cell pack assemblies (there are two place holder cells that are not part of the life test electrical circuit). The test pack is configured to simulate the conductive thermal design of the spacecraft battely, including: conductive aluminum sleeves, 3-cell pack aluminum baseplate, and honeycomb panel all mounted to a liquid (-5 C) cold plate. The entire assembly is located in a thermal chamber operating at +3 C. The accelerated stress test unit consists of five cells mounted in machined aluminum test sleeves and is operating at +10 C. The real-time LEO life test battery has met all performance requirements through the first 13,000 cycles, including: end of charge and discharge cell voltages and voltage gradients; end of chalge and discharge cell pressures; within cell and between cell temperature gradients; discharge capacity; current and power levels; and all chalge parameters. The accelerated stress test battely has completed over 5900 cycles as of 9/11/96. This paper reports both battery performances as a function of cycle life, with individual cell performance comparisons repolted for selected cycles in both tests.

Bennett, C. W.↗

EOS-AM1 Nickel Hydrogen Cell

This paper reports the interim results of the Earth Observing System AM-1 project (EOS-AM-1) nickel hydrogen cell life test being conducted under contract to National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) at the Lockheed Martin Missile and Space (LMMS) facility in East Windsor, NJ; and at COMSAT Labs., Clarksburg, MD. The purpose of die tests is to verify that the EOS-AM-1 cell design can meet five years of real-time Low Earth Orbit (LEO) cycling. The tests include both real-time LEO and accelerated stress tests. At LMMS, the first real-time LEO simulated 99 minute orbital cycle started on February 7, 1994 and the test has been running continuously since that time, with 18,202 LEO cycles completed as of September 1, 1997. Each cycle consists of a 64 minute charge (VT at 1.507 volts per cell, 1.06 C/D ratio, followed by 0.6 ampere trickle charge) and a 35 minute constant power discharge at 177 watts (22.5% DOD). At COMSAT, the accelerated stress test consists of 90 minute orbital cycles at 60% DOD with a 30 minute discharge at 60 amperes and a 60 minute charge at 40 amperes (VT at 1.54 volts per cell to 1.09 C/D ratio, followed by 0.6 ampere trickle charge). The real-time LEO life test battery consists of seven, 50AH (nameplate rating) Eagle-Picher, Inc. (EPI) Mantech cells manufactured into three, 3-cell pack assemblies (there are two place holder cells that are not part of the life test electrical circuit). The test pack is configured to simulate the conductive thermal design of the spacecraft battery, including: conductive aluminum sleeves, 3-cell pack aluminum baseplate, and honeycomb panel all mounted to a liquid (-5 C) cold plate. The entire assembly is located in a thermal chamber operating at +30 C. The accelerated stress test unit consists of five cells mounted in machined aluminum test sleeves and is operating at +10 C. The real-time LEO life test battery has met all performance requirements through the first 18,202 cycles, including: end of charge mid discharge cell voltages and voltage gradients; end of charge and discharge cell pressures; within cell and between cell temperature gradients; discharge capacity; current and power levels; and all charge parameters. The accelerated stress test battery has completed 11,998 cycles when the test was terminated. The stress test unit met all test parameters. This paper reports battery perfortnances as a funcfion of cycle life for both the real-time LEO and the accelerated life test regimes.

Bennett, Charles W.↗

EOS--AM1 Nickel Hydrogen Cell Interim Life Test Report

This paper reports the interim results of the Earth Observing System AM-1 project (EOS-AM-1) nickel hydrogen cell life test being conducted under contract to National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) at the Lockheed Martin Missiles and Space (LMMS) facility in East Windsor, NJ; and at COMSAT Labs., Clarksburg, MD. The purpose of the tests is to verify that the EOS-AM-1 cell design can meet five years of real-time Low Earth Orbit (LEO) cycling. The tests include both real-time LEO and accelerated stress tests. At LMMS, the first real-time LEO simulated 99 minute orbital cycle started on February 7, 1994 and the test has been running continuously since that time, with 18202 LEO cycles completed as of September 1, 1997. Each cycle consists of a 64 minute charge (VT at 1.507 volts per cell. 1.06 C/D ratio, followed by 0.6 ampere trickle charge) and a 35 minute constant power discharge at 177 watts (22.5% DOD). At COMSAT, the accelerated stress test consists of 90 minute orbital cycles at 60% DOD with a 30 minute discharge at 60 amperes and a 60 minute charge at 40 amperes (VT at 1.54 volts per cell to 1.09 C/D ratio, followed by 0.6 ampere trickle charge). The real-time LEO life test battery consists of seven, 50AH (nameplate rating) Eagle-Picher, Inc. (EPI) Mantech cells manufactured into three. 3-cell pack assemblies (there are two place holder cells that are not part of the life test electrical circuit). The test pack is configured to simulate the conductive thermal design of the spacecraft battery, including: conductive aluminum sleeves, 3-cell pack aluminum baseplate, and honeycomb panel all mounted to a liquid (-5 C) cold plate. The entire assembly is located in a thermal chamber operatina at +30 C. The accelerated stress test unit consists of five cells mounted in machined aluminum test sleeves and is operating at +10 C. The real-time LEO life test battery has met all performance requirements throuch the first 18,202 cycles, including: end of chargee and discharge cell voltages and voltace -radients; end of charge and discharge cell pressures; within cell and between cell temperature gradients; discharge capacity; current and power levels; and all charge parameters. The accelerated stress test battery has completed 11,998 cycles when the test was terminated. The stress test unit met all test parameters. This paper reports battery performances as a function of cycle life for both the real time LEO and the accelerated life test regimes.

Bennett, C. W.↗

Experimental Simulation of Turbine-Exhaust Oxygen Recovery

In some liquid-propellant rocket engines, the liquid-oxygen boost pump is driven by a turbine that is powered by high-pressure gaseous oxygen. Once it exits the turbine, this gaseous oxygen can be salvaged by injecting it into the subcooled liquid oxygen exiting the boost pump. If the main LOX pump is to function correctly under these circumstances, complete condensation of the gaseous oxygen must quickly follow its injection into the boost-pump discharge. The current investigation uses steam and water in a simple rig that allows the condensation process to be visualized and quantified. This paper offers dimensionless-parameter correlations of the data and trends observed.

Clark, Jim A.↗

A theoretical analysis of vacuum arc thruster performance

In vacuum arc discharges the current is conducted through vapor evaporated from the cathode surface. In these devices very dense, highly ionized plasmas can be created from any metallic or conducting solid used as the cathode. This paper describes theoretical models of performance for several thruster configurations which use vacuum arc plasma sources. This analysis suggests that thrusters using vacuum arc sources can be operated efficiently with a range of propellant options that gives great flexibility in specific impulse. In addition, the efficiency of plasma production in these devices appears to be largely independent of scale because the metal vapor is ionized within a few microns of the cathode electron emission sites, so this approach is well-suited for micropropulsion.

thruster↗

Azimuthal Spoke Propagation in Hall Effect Thrusters

Spokes are azimuthally propagating perturbations in the plasma discharge of Hall Effect Thrusters (HETs) that travel in the E x B direction and have been observed in many different systems. The propagation of azimuthal spokes are investigated in a 6 kW HET known as the H6 using ultra-fast imaging and azimuthally spaced probes. A spoke surface is a 2-D plot of azimuthal light intensity evolution over time calculated from 87,500 frames/s videos. The spoke velocity has been determined using three methods with similar results: manual fitting of diagonal lines on the spoke surface, linear cross-correlation between azimuthal locations and an approximated dispersion relation. The spoke velocity for three discharge voltages (300, 400 and 450 V) and three anode mass flow rates (14.7, 19.5 and 25.2 mg/s) yielded spoke velocities between 1500 and 2200 m/s across a range of normalized magnetic field settings. The spoke velocity was inversely dependent on magnetic field strength for low B-field settings and asymptoted at B-field higher values. The velocities and frequencies are compared to standard drifts and plasma waves such as E x B drift, electrostatic ion cyclotron, magnetosonic and various drift waves. The empirically approximated dispersion relation yielded a characteristic velocity that matched the ion acoustic speed for 5 eV electrons that exist in the near-anode and near-field plume regions of the discharge channel based on internal measurements. Thruster performance has been linked to operating mode where thrust-to-power is maximized when azimuthal spokes are present so investigating the underlying mechanism of spokes will benefit thruster operation.

Cylindrical Hall Thruster (CHT)↗

Propulsion System Testing for the Iodine Satellite (iSAT) Demonstration Mission

CUBESATS are relatively new spacecraft platforms that are typically deployed from a launch vehicle as a secondary payload, providing low-cost access to space for a wide range of end-users. These satellites are comprised of building blocks having dimensions of 10x10x10 cm cu and a mass of 1.33 kg (a 1-U size). While providing low-cost access to space, a major operational limitation is the lack of a propulsion system that can fit within a CubeSat and is capable of executing high delta v maneuvers. This makes it difficult to use CubeSats on missions requiring certain types of maneuvers (i.e. formation flying, spacecraft rendezvous). Recently, work has been performed investigating the use of iodine as a propellant for Hall-effect thrusters (HETs) 2 that could subsequently be used to provide a high specific impulse path to CubeSat propulsion. 3, 4 Iodine stores as a dense solid at very low pressures, making it acceptable as a propellant on a secondary payload. It has exceptionally high ρIsp (density times specific impulse), making it an enabling technology for small satellite near-term applications and providing the potential for systems-level advantages over mid-term high power electric propulsion options. Iodine flow can also be thermally regulated, subliming at relatively low temperature (less than 100 C) to yield I2 vapor at or below 50 torr. At low power, the measured performance of an iodine-fed HET is very similar to that of a state-of-the-art xenon-fed thruster. Just as importantly, the current-voltage discharge characteristics of low power iodine-fed and xenon-fed thrusters are remarkably similar, potentially reducing development and qualifications costs by making it possible to use an already-qualified xenon-HET PPU in an iodine-fed system. Finally, a cold surface can be installed in a vacuum test chamber on which expended iodine propellant can deposit. In addition, the temperature doesn't have to be extremely cold to maintain a low vapor pressure in the vacuum chamber (it is under 10(exp -6) torr at −75 C), making it possible to 'cryopump' the propellant with lower-cost recirculating refrigerant-based systems as opposed to using liquid nitrogen or low temperature gaseous helium cryopanels. An iodine-based system is not without its challenges. The primary challenge is that the entire feed system must be maintained at an elevated temperature to prevent the iodine from depositing (transitioning from the gas phase directly back into the solid phase), which will block the propellant feed lines. Furthermore, deposition will occur unless the temperature in the lines is not greater than the temperature of the propellant reservoir. The flow rate can be controlled by adjusting the heating applied to the reservoir, but as with any thermal control there is a relatively slow response to changes in the heating rate. In the present paper, we describe the propulsion and propellant feed system for the iodine satellite (iSAT) flight demonstration mission. The system is based around the Busek BHT-200 Hall thruster, which has been modified for chemical compatibility with iodine vapor. While the gross propellant flow rate is maintained by the heated propellant reservoir, the flow to the anode and cathode are adjusted using two heated Vacco proportional flow control valves (PFCV), which provide very fast response on the flow rate adjustment. The flight mission design layout will be presented, showing how the system will be packaged into the overall 12-U spacecraft and the techniques being employed to protect the remaining spacecraft hardware from the propulsion system (e.g., plasma impingement, iodine deposition, thermal loads). In addition to the flight system design, results of testing the thruster and cathode with both operating on iodine propellant are presented. The tests are conducted on a thrust stand (see Fig. 1) in a large vacuum chamber containing a beam dump chilled to below -100 C to 'cryopump' the propellant. The thruster performance during these tests is presented, with these data used to evaluate the feed system and guide further refinements. Results of relatively long duration testing are presented to demonstrate the capability to operate for the length of the iSAT mission and to perform a number of re-starts as will be required by the mission concept of operations.

Polzin, Kurt A.↗

Engineering Model Propellant Feed System Development for an Iodine Hall Thruster Demonstration Mission

CUBESATS are relatively new spacecraft platforms that are typically deployed from a launch vehicle as a secondary payload, providing low-cost access to space for a wide range of end-users. These satellites are comprised of building blocks having dimensions of 10x10x10 cu cm and a mass of 1.33 kg (a 1-U size). While providing low-cost access to space, a major operational limitation is the lack of a propulsion system that can fit within a CubeSat and is capable of executing high (Delta)v maneuvers. This makes it difficult to use CubeSats on missions requiring certain types of maneuvers (i.e. formation flying, spacecraft rendezvous). Recently, work has been performed investigating the use of iodine as a propellant for Hall-effect thrusters (HETs) 2 that could subsequently be used to provide a high specific impulse path to CubeSat propulsion. 3, 4 Iodine stores as a dense solid at very low pressures, making it acceptable as a propellant on a secondary payload. It has exceptionally high ρIsp (density times specific impulse), making it an enabling technology for small satellite near-term applications and providing the potential for systems-level advantages over mid-term high power electric propulsion options. Iodine flow can also be thermally regulated, subliming at relatively low temperature (< 100 C) to yield I2 vapor at or below 50 torr. At low power, the measured performance of an iodine-fed HET is very similar to that of a state-of-the-art xenon-fed thruster. Just as importantly, the current-voltage discharge characteristics of low power iodine-fed and xenon-fed thrusters are remarkably similar, potentially reducing development and qualifications costs by making it possible to use an already-qualified xenon-HET PPU in an iodine-fed system. Finally, a cold surface can be installed in a vacuum test chamber on which expended iodine propellant can deposit. In addition, the temperature doesn't have to be extremely cold to maintain a low vapor pressure in the vacuum chamber (it is under 10(exp −6) torr at −75 C), making it possible to 'cryopump' the propellant with lower-cost recirculating refrigerant-based systems as opposed to using liquid nitrogen or low temperature gaseous helium cryopanels. In the present paper, we describe the design and testing of the engineering model propellant feed system for iSAT (see Fig. 1). The feed system is based around an iodine propellant reservoir and two proportional control valves (PFCVs) that meter the iodine flow to the cathode and anode. The flow is split upstream of the PFCVs to both components can be fed from a common reservoir. Testing of the reservoir is reported to demonstrate that the design is capable of delivering the required propellant flow rates to operate the thruster. The tubing and reservoir are fabricated from hastelloy to resist corrosion by the heated gaseous iodine propellant. The reservoir, tubing, and PFCVs are heated to ensure the sublimed propellant will not re-deposit within the feed system. Heating is accomplished through a number of individual zones to control the overall power expended on heating the system and insulation is employed to minimize the amount of power used to heat the system prior to thruster operation.

Polzin, Kurt A.↗

Global irrigation contribution to wheat and maize yield

Irrigation is the largest sector of human water use and an important option for increasing crop production and reducing drought impacts. However, the potential for irrigation to contribute to global crop yields remains uncertain. Here, we quantify this contribution for wheat and maize at global scale by developing a Bayesian framework integrating empirical estimates and gridded global crop models on new maps of the relative difference between attainable rainfed and irrigated yield (ΔY). At global scale, ΔY is 34 ± 9% for wheat and 22 ± 13% for maize, with large spatial differences driven more by patterns of precipitation than that of evaporative demand. Comparing irrigation demands with renewable water supply, we find 30–47% of contemporary rainfed agriculture of wheat and maize cannot achieve yield gap closure utilizing current river discharge, unless more water diversion projects are set in place, putting into question the potential of irrigation to mitigate climate change impacts.

Irrigation↗

Performance and High-Speed Characterization of a 100-kW Nested Hall Thruster

The performance of a three-channel, 100-kW class nested Hall thruster was evaluated on xenon propellant for total powers up to 102 kW. The thruster demonstrated stable operation in all seven available channel combinations at discharge voltages from 300 V to 500 V and three different current densities. The resulting test matrix contained forty-six unique conditions ranging from 5 to 102 kW total power and 16 to 247 A discharge current. At each operating condition, thrust and telemetry was measured, and from these measurements specific impulse and efficiency were calculated. All seven channel combinations showed similar performance at a given discharge voltage and current density. The largest thrust recorded was 5.4 N ± 0.1 N at 99 kW, 400 V discharge voltage. Total efficiency and specific impulse ranged from 0.54 to 0.67 ± 0.03 and 1800 seconds to 2650 seconds ± 60 seconds, respectively. It was found that the thrust of the three channels firing together was not larger than the sum of each channel firing individually. Discharge current oscillations were also characterized with peak-to-peak and root-mean-square values and with high-speed camera analysis, which provide insight into how the discharge channels oscillate, and how those oscillations are affected by the presence of other operating channels. The implications of these results are discussed in the context of operation beyond 100 kW, as well as the general viability of NHT technology for future mission applications.

High-power↗

High-Power Performance of a 100-kW Class Nested Hall Thruster

The performance of a three-channel, 100-kW class nested Hall thruster was evaluated on xenon propellant for total powers up to 102 kW at NASA Glenn Research Center. The thruster demonstrated stable operation in all seven available channel combinations at discharge voltages from 300 V to 500 V and three different current densities. The resulting test matrix contained forty-six unique conditions ranging from 5 to 102 kW total power and 16 to 247 A discharge current. At each operating condition, thruster performance was measured, and from these measurements specific impulse and efficiency were calculated. All seven channel combinations showed similar performance at a given discharge voltage and current density. The largest thrust recorded was 5.4 N ± 0.1 N at 99 kW, 400 V discharge voltage. Total efficiency and specific impulse ranged from 0.54 to 0.67 ± 0.03 and 1800 seconds to 2650 seconds ± 60 seconds, respectively. It was found that the thrust of the three channels firing together was not larger than the sum of each channel firing individually. Discharge current oscillations were also characterized with peak-to-peak and root-mean-square values and with power spectral density analysis. The implications of these results are discussed in the context of operation beyond 100 kW, as well as the general viability of NHT technology for future mission applications.

Hall, Scott J.↗

Current sheet Formation in a Conical Theta Pinch Faraday Accelerator with Radio-Frequency Assisted Discharge

The inductive formation of current sheets in a conical theta pinch FARAD (Faraday Accelerator with Radio-frequency Assisted Discharge) thruster is investigated experimentally with time-integrated photography. The goal is to help in understanding the mechanisms and conditions controlling the strength and extent of the current sheet, which are two indices important for FARAD as a propulsion concept. The profiles of these two indices along the inside walls of the conical acceleration coil are assumed to be related to the profiles of the strength and extent of the luminosity pattern derived from photographs of the discharge. The variations of these profiles as a function of uniform back-fill neutral pressure (with no background magnetic field and all parameters held constant) provided the first clues on the nature and qualitative dependencies of current sheet formation. It was found that there is an optimal pressure for which both indices reach a maximum and that the rate of change in these indices with pressure differs on either side of this optimal pressure. This allowed the inference that current sheet formation follows a Townsend-like breakdown mechanism modified by the existence of a finite pressure-dependent radio-frequency-generated electron density background. The observation that the effective location of the luminosity pattern favors the exit-half of the conical coil is explained as the result of the tendency of the inductive discharge circuit to operate near its minimal self-inductance. Movement of the peak in the luminosity pattern towards the upstream side of the cone with increasing pressure is believed to result from the need of the circuit to compensate for the increase in background plasma resistivity due to increasing pressure.

Hallock, Ashley K.↗

Implementation and Initial Validation of a 100-Kilowatt Class Nested-Channel Hall Thruster

The X3 is a 100-kilowatt class nested-channel Hall thruster developed by the Plasmadynamics and Electric Propulsion Laboratory at the University of Michigan in collaboration with the Air Force Research Laboratory and NASA. The cathode, magnetic circuit, boron nitride channel rings, and anodes all required specific design considerations during thruster development, and thermal modeling was used to properly account for thermal growth in material selection and component design. A number of facility upgrades were required at the University of Michigan to facilitate operation of the X3. These upgrades included a re-worked propellant feed system, a completely redesigned power and telemetry break-out box, and numerous updates to thruster handling equipment. The X3 was tested on xenon propellant at two current densities, 37% and 73% of the nominal design value. It was operated to a maximum steady-state discharge power of 60.8 kilowatts. The tests presented here served as an initial validation of thruster operation. Thruster behavior was monitored with telemetry, photography and high-speed current probes. The photography showed a uniform plume throughout testing. At constant current density, reductions in mass flow rate of 18% and 26% were observed in the three-channel operating configuration as compared to the superposition of each channel running individually. The high-speed current probes showed that the thruster was stable at all operating points and that the channels influence each other when more than one is operating simultaneously. Additionally, the ratio of peak-to-peak AC-coupled discharge current oscillations to mean discharge current did not exceed 51% for any operating points reported here, and did not exceed 17% at the higher current density.

High Power↗

Plasma Emission Characteristics from a High Current Hollow Cathode in an Ion Thruster Discharge Chamber

The presence of energetic ions produced by a hollow cathodes operating at high emission currents (greater than 5A) has been documented in the literature. In order to further elucidate these findings, an investigation of a high current cathode operating in an ion thruster discharge chamber has been undertaken. Using Langmuir probes, a low energy charged particle analyzer and emission spectroscopy, the behavior of the near-cathode plasma and the emitted ion energy distribution was characterized. The presence of energetic ions was confirmed. It was observed that these ions had energies in excess of the discharge voltage and thus cannot be simply explained by ions falling out of plasma through a potential difference of this order. Additionally, evidence provided by Langmuir probes suggests the existence of a double layer essentially separating the hollow cathode plasma column from the main discharge. The radial potential difference associated with this double layer was measured to be of order the ionization potential.

Foster, John E.↗

Modeling taper charge with a non-linear equation

Work aimed at modeling the charge voltage and current characteristics of nickel-cadmium cells subject to taper charge is presented. Work reported at previous NASA Battery Workshops has shown that the voltage of cells subject to constant current charge and discharge can be modeled very accurately with the equation: voltage = A + (B/(C-X)) + De to the -Ex where A, B, D, and E are fit parameters and x is amp-hr of charge removed during discharge or returned during charge. In a constant current regime, x is also equivalent to time on charge or discharge.

Mcdermott, P. P.↗

Energetic ion production and electrode erosion in hollow cathode discharges

Ions with energies significantly in excess of the discharge voltage have been reported in high current hollow cathode discharges. Models of DC potential hills downstream of the cathode and ion acoustic instabilities in a double layer postulated in the cathode orifice have been proposed to explain these energetic ions, but have not been substantiated in experiments.

ion thruster↗