Ion Thruster

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Description

The Ion Thruster class models an electric propulsion system using ionized propellant to generate thrust. Unlike chemical thrusters, ion thrusters determine required input power based on desired thrust rather than mass flow rate. This class is inherits from the abstract Thruster base class.

The class provides functionality to:

• Compute thrust from available electrical power.
• Determine electrical power requirements based on desired thrust.
• Calculate body-frame force and impulse for spacecraft dynamics.

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Module Implementation

Thrust Calculation from Power

The thrust $F$ produced by an ion thruster is related to the input power $P$, the exhaust velocity $V_e$, and thruster efficiency $\eta$ as:

$$F=\frac{2\eta P}{v_e}$$

where:

• $F$ = thrust N
• $P$ = available electrical power W
• $\eta$ = thruster efficiency (0 < η ≤ 1)
• $v_e$= exhaust velocity m/s

Exhaust velocity $v_e$ is calculated from the specific impulse $I_{sp}$ as:

$$v_e=I_{sp}.g_0$$

where:

• $I_{sp}$ = specific impulse s
• $g_0$ = standard gravitational acceleration (9.80665 m/s²)

Power Requirement from Desired Thrust

To determine the power required to achieve a specified thrust, the inverse of the thrust equation is used:

$$P=\frac{F{v}_e}{2\eta }$$

where:

• $P$ = desired power W
• $F$= desired thrust N

Body-Frame Force Calculation

The thrust in the spacecraft body frame is calculated as:

$${\mathbf{F}}_B={\hat{\mathbf{d}}}_B\cdot F\cdot (1-\text{DispersedFactor})$$

where:

• ${\mathbf{F}}_B$ = body-frame force vector N
• ${\hat{\mathbf{d}}}_B$ = thrust direction unit vector in body frame
• $\text{DispersedFactor}$= factor accounting for thruster misalignment or beam dispersion

This ensures that the thrust vector is appropriately scaled and aligned with the thruster orientation.

Impulse Calculation

The body-frame impulse per unit mass is given by:

$$\mathbf{I}=\frac{{\mathbf{F}}_B}{v_e}$$

This is used in spacecraft dynamics to update velocities according to the applied thrust.

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Assumptions/Limitations

• Steady-State Operation: The thruster is assumed to operate at steady state; transient startup or throttling dynamics are not modeled.
• Linear Efficiency Model: Thruster efficiency $\eta$ is assumed constant and independent of input power or thrust level.
• Ideal Power Conversion: Power losses outside the thruster (e.g., transmission, bus inefficiencies) are not considered.
• Single Propellant: The thruster model assumes a single ionized propellant (e.g., Xenon), and no chemical reactions are involved.
• Negligible Beam Divergence: Dispersed Factor accounts for minor deviations, but large plume effects are not modeled.
• No Thermal or Structural Modeling: The code does not model thruster heating or structural limits.
• No Detailed Plasma Physics: Ionization dynamics, space charge effects, and plasma plume interactions are not considered.
• Power Model Dependency: Power Model must exist for proper calculation; null or missing models will halt computations.
• Zero or Negative Efficiency: If Efficiency <= 0, thrust is considered zero, which may not reflect real-world partial operation.
• Vector Normalization: Force calculation assumes non-zero force magnitude for impulse calculation; otherwise, a zero vector is returned.

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References

[1] Choueiri, E. Y. (2009). A Critical History of Electric Propulsion: The First 50 Years (1906–1956). Journal of Propulsion and Power, 20(2), 193–203.

[2] Sutton, G. P., & Biblarz, O. (2017). Rocket Propulsion Elements (9th ed.). Wiley.

[3] Wertz, J. R., Everett, D. F., & Puschell, J. J. (2011). Space Mission Engineering: The New SMAD (2nd ed.). Microcosm Press.