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130 Chapter 4 It is necessary to specify either the discharge current or the beam current in order to calculate the plasma density in the discharge chamber. The grid transparency is obtained from the grid codes (called “optics codes”). Several of these codes, such as the Jet Propulsion Laboratory (JPL) CEX ion optics codes [34,35] that we use, are described in Chapter 5. The cathode voltage drop is either measured inside the hollow cathode [36] or calculated using a separate 2-D hollow cathode plasma model [37] that will be described in Chapter 6. Discharge chamber behavior is characterized by “performance curves,” which were described in Chapter 2 and are graphs of discharge loss versus mass utilization efficiency. These curves plot the electrical cost of producing beam ions as a function of the propellant utilization efficiency, and they give useful information on how well the plasma generator works. Performance curves are normally taken at constant beam current and discharge voltage so that the efficiency of producing and delivering ions to the beam is not masked by changes in the discharge voltage or average plasma density at the grids. Calculating performance curves using Eq. (4.3-60) requires iteration of the solutions for the electron temperature, discharge current, and/or beam current in the above equations. To measure the discharge loss versus mass utilization in thrusters, the discharge current, total gas flow, and gas flow split between the cathode and main discharge chamber are normally varied to produce a constant beam current and discharge voltage as the mass utilization efficiency changes. This means that a beam current and mass utilization operating point can be specified, which determines the neutral gas density in the discharge chamber from Eq. (4.3-35) and the average plasma density in the discharge chamber from the Bohm current in Eq. (4.3-9). If an initial discharge current is then specified, the primary electron density can be calculated from Eq. (4.3-45) and the electron temperature obtained by finding a solution to Eq. (4.3-36). These parameters are used to solve for the discharge loss, which is evaluated from the given beam current, discharge voltage, and discharge loss. A program is iterated until a discharge current is found that produces the correct discharge loss at the specified beam current. An example of performance curves calculated using this model and compared to measured curves for the NEXIS ion thruster [38] are shown in Fig. 4-18. The discharge loss was measured for three different discharge voltages during operation at 4 A of beam current. The 180-eV/ion discharge loss at the 26.5-V discharge voltage required that the cathode produce a discharge current of 27.8 A to generate the 4 A of ion beam current.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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