Selección natural como conjunto de hechos e inferencias

An annular electromagnetic launcher model was developed to simplify the physics of a translating plasmoid using a circuit-based approach. The plasmoid was approximated as a rigid conducting slug, expelled from the coils by a Lorentz force. A series of design studies was conducted to understand how inputs for the model such as cone angle and inner coil radius affected the resulting plasmoid’s trajectory and the energy efficiency of the translation process. Using the results from these studies, a design was selected for the XOCOT-T3 and tested with the launcher model to ensure the plasmoid was able to translate from the discharge coils during its lifetime. The final design selected the 225 µF capacitor bank for a discharge frequency of 10 kHz, with the 43.5 µF, 20 kHz bank as the alternate. The cone angle was minimized to 2 degrees and the inner coil radius was maximized at 7.2 cm. The minimum energy required for translation with the 225 µF bank was 200 J; the minimum energy using the 43.5 µF bank was 600 J. The expected plasmoid velocity and energy efficiency of the final design was estimated at 100 - 150 km/s with an energy efficiency of 26 - 35%. The simulated plasmoid mass of 1.1x10−8kg, resulted in a directed impulse bit (momentum) of 1.1 mN-s to 1.7 mN-s.

The final XOCOT-T3 design selected four turns for the outer and inner coil. Magnetic field simulations in COMSOL revealed that the coil introduced distortions in the field from current interactions between nearby turns. Magnetic field simulations were conducted with a conducting plasma between the coils, producing a reversed field magnetic field on the inner wall compared to the vacuum field. The appearance of this reversed field in the experiment will provide evidence that a conducting reversed-field plasmoid is present in annulus. Further simulations with a moving conductive region between the coils,

mimicing a translating plasmoid, demonstrated typical magnetic field signatures expected by a translating plasmoid. These signatures will aid in diagnosing plasmoid motion in the experiment.

The design studies uncovered new insights into the design of annular launchers, including the need for small cone angles on the outer coil. Shallow cone angles are required for efficient annular launchers as they align the region of peak acceleration (dM/dz) of the outer coil with the inner coil. Larger cone angles extended the region of peak acceleration for the outer coil back towards the throat of the coil; while the region of peak acceleration for the inner coil remains near the downstream end of the coil. Aligning the regions of peak acceleration for the inner and outer coil maximizes the total dM/dz of the system, which is directly proportional to the Lorentz force. This means that the maximum possible Lorentz force can be achieved by timing the passage of the plasmoid through this region when the coil currents and plasmoid current are at their peak. Maximizing the Lorentz force is a direct payoff to energy efficiency, since it allows the plasmoid to exit with the maximum velocity.

Maximum efficiency also arises when the inner coil is the largest possible diameter. This brings the coil in closer contact with the plasmoid for improved coupling, increases the inductance of the inner coil, and drives more current to the outer coil to improve its effectiveness. All three effects work to maximize the Lorentz force and thus, energy efficiency. The drawback to larger inner coil diameters is that it increases the chance of wall contact with the plasma since finite thickness insulators must be placed over the coils for electrical protection. Wall contact is to be avoided in pulsed inductive plasma systems as it leads to massive cooling of the plasma and disruption of the current configuration.

launcher geometries to perfect timing. For maximum efficiency, the plasma must arrive at the region of peak acceleration (peak dM/dz) when the coil currents and plasma current peak. This was discovered in the energy study for the annular model, but can be expanded to other geometries as well. The timing can be adjusted by changing the initial energy to control the initial plasmoid acceleration. Unpredictable factors such as a variation in mass of the plasmoid and a variation in plasmoid size can alter the optimal input energy from model predictions. It is highly likely that empirical studies will be required to find the optimal energy for each device to attain maximum efficiency.

The sensitivity of energy efficiency to timing of the plasmoid’s trajectory through the region of peak acceleration is unfortunate for AFRCs. Experimental studies have demonstrated that the lifetime of an AFRC is limited to the quarter-cycle of the discharge. This lifetime definition is based on when magnetic field reversal is lost on the inner wall. In reality, the reversed field begins to decay before this time implying that the plasma current begins to degrade as well and the true lifetime is shorter than the quarter-cycle of the discharge. This means that an AFRC must be ejected from the coils when the plasma currents peak, sometime before the coil currents peak. This severely limits the energy efficiency of the system, since all three currents must be at their peak together for maximum efficiency. These observations are not limited to the annular geometry. Conical θ -pinch launchers have similar acceleration physics and may be sensitive to a similar timing constraint. While launcher-types studies have been previously conducted for conical θ -pinch designs [2], lifetime considerations were not included in this analysis.

The exit velocity of the AFRC plasmoid predicted by these studies is much higher than other PIPT devices. The range of exit velocities demonstrated in other experiments discussed in Section 2.3 is between 10-20 km/s. The exit velocities predicted by the

launcher model were in excess of 100 km/s. These extreme exit velocities are the consequence of a fairly high discharge frequency (10 kHz). The plasmoid must travel the full length of the coil in less than 25 µs, accelerating from a standstill only when the currents are high enough to result in a sufficient Lorentz force. Lengthening the quarter cycle by reducing the frequency will likely lower the exit velocity, though the competing effect of slower-building plasma currents may result in a longer initial translation delay.

Despite the numerous insights the annular electromagnetic launcher model results have uncovered, many of these are based around the assumption of a rigid plasmoid-slug which maintains its shape even as it travels downstream. This assumption is unlikely to hold in a plasma experiment, as changing fluid properties will dominate the overall structure of the plasmoid. Experimental hardware is required to fully test the capability of an AFRC-based thruster. Data from the experiment can be compared to the model to understand how well this model predicts plasmoid behavior.

Chapter 5

Experiment, Facilities, and Diagnostics

This chapter discusses the experimental setup, facilties, and diagnostics used in this research. Section 5.1 describes the XOCOT-T3 experiment, including specific details about the discharge circuit, the pre-ionization circuit, switching hardware, gas feed system, vacuum systems, safety considerations, and experimental operating procedures. Detailed information about the coil construction is provided, along with impedance measurements of discharge circuit components. The diagnostics used in this work are discussed in Section 5.2. The diagnostic tools include current and voltage probes, magnetic field diagnostics, plasma probes, and single frame photography. An indepth look at magnetic probe theory is provided in Section 5.2.2 along with a discussion of probe calibration techniques and probe construction. Plasma probes, or Langmuir probes, are discussed in Section 5.2.3. The implementation of these diagnostics in measuring the plasmoid’s velocity, impulse-bit, and energy efficiency is discussed in Section 5.3.