3.2. Description of thrust stand

The impulse bits in the six cases of Table 1 are measured by a calibrated thrust stand. The calibrated thrust-stand utilizing inverted pendulum techniques is developed and applied to estimate μNs-class impulses. Schematic of experimental setup for impulse-bit measurement is given in Figure 3. The thruster was settled onto the inverted pendulum. As an ns pulsed Nd:YAG laser beam passes through a quartz glass window and lens, the thruster is initialized, and the plasma is produced. The inverted pendulum swung on a knife-edge immediately. The motion of the pendulum is attenuated by an electromagnetic damper device subsequently. And the pendular angular is measured by an optical non-contacting measurement method. A He-Ne laser beam penetrated through a quartz glass window and irradiated onto a moving mirror settled near the knife-edge. The mirror rotated along with the motion of pendulum. The laser beam eventually irradiates into a position sensitive detector (PSD) after passing through several mirrors as shown in Figure 3.

For measuring the impulse bits, the calibration procedures are conducted. Because of the zero drift phenomenon and other influencing factors that gradually change the equilibrium position of pendulum in experiments, especially in evacuation and gas charging procedure of the vacuum chamber, the measurement system should be calibrated before or after impulse bit measurements are implemented. The electromagnetic calibration subsystem is proposed as shown in Figure 4 and described herein. A pulsed Ampere force is generated by a couple of parallel permanent magnet (NdFeB) plates and live wires as shown in Figure 4, and utilized to simulate the pulsed thrust of thruster. The pair of permanent magnet plates is settled behind the thruster, and the height of Ampere force action spot is set to be the same with the action spot of pulsed thrust of thruster. The distance between the couple of magnets is set 5 mm, and the crest value and duration of current in the conducting wires are controlled by a function

Case Propellants d1 (mm) d2 (mm) A<sup>0</sup> B<sup>0</sup> A B

I Aluminum 20 10 4.8666E�3 5.6211E1 �6.5748E�4 2.2113E�2 II Aluminum 30 10 �1.2289E�3 2.4758E�2 III Aluminum 30 15 1.5489E�4 2.5930E�2 IV Aluminum 30 20 1.0816E�3 2.8182E�2 V Aluminum 40 20 1.1685E�3 2.8730E�2 VI PTFE 20 10 3.5247E�3 2.3624E�2

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a. The relationship of Ampere force F and the volts d.c. output X of the function generator is tested by using an electronic balance (Mettler Toledo XS205, minimum mass 10 μg). The

where the coefficients A<sup>0</sup> and B<sup>0</sup> are obtained after the calibration procedure.

ð15Þ

generator as shown in Figure 4.

relationship can be expressed as:

The detailed calibration procedure is described herein.

Figure 4. Schematic illustration of the electromagnetic calibration method.

Table 1. Six cases and coefficients obtained in calibration procedures.

Figure 3. Schematic illustration of the impulse bit measurement system.


Table 1. Six cases and coefficients obtained in calibration procedures.

3. Experimental setup

probe (Tektronix P5100).

3.2. Description of thrust stand

3.1. Measurement setup for discharge arcs

196 Plasma Science and Technology - Basic Fundamentals and Modern Applications

As shown in Figure 3, a ns-pulsed Nd:YAG laser (InnoLas Corp. SpitLight 600, wavelength: 1064 nm, pulse energy: ~600 mJ, pulse width: 7 ns) is used for laser ablation of propellants. The laser pulse is irradiated into a vacuum chamber (vacuum degree: <5.0 <sup>10</sup><sup>4</sup> Pa) through a quartz window and focused on the propellant with a focusing lens (f = 400 mm). The thruster is ignited and initiated by the ns-pulsed laser. Discharge arcs formed between the electrodes of thruster. The discharge current is monitored with a current monitor (Rogowski Coil, CWT150, sensitivity: 0.2 mV/A, maximum current: 30.0 kA) and a digital oscilloscope (Tektronix DPO 4340). The discharge voltage between the electrodes is measured using a standard high-voltage

The impulse bits in the six cases of Table 1 are measured by a calibrated thrust stand. The calibrated thrust-stand utilizing inverted pendulum techniques is developed and applied to estimate μNs-class impulses. Schematic of experimental setup for impulse-bit measurement is given in Figure 3. The thruster was settled onto the inverted pendulum. As an ns pulsed Nd:YAG laser beam passes through a quartz glass window and lens, the thruster is initialized, and the plasma is produced. The inverted pendulum swung on a knife-edge immediately. The motion of the pendulum is attenuated by an electromagnetic damper device subsequently. And the pendular angular is measured by an optical non-contacting measurement method. A He-Ne laser beam penetrated through a quartz glass window and irradiated onto a moving mirror settled near the knife-edge. The mirror rotated along with the motion of pendulum. The laser beam eventually irradiates into a position sensitive detector (PSD) after passing through several mirrors as shown in Figure 3.

For measuring the impulse bits, the calibration procedures are conducted. Because of the zero drift phenomenon and other influencing factors that gradually change the equilibrium position

Figure 3. Schematic illustration of the impulse bit measurement system.

Figure 4. Schematic illustration of the electromagnetic calibration method.

of pendulum in experiments, especially in evacuation and gas charging procedure of the vacuum chamber, the measurement system should be calibrated before or after impulse bit measurements are implemented. The electromagnetic calibration subsystem is proposed as shown in Figure 4 and described herein. A pulsed Ampere force is generated by a couple of parallel permanent magnet (NdFeB) plates and live wires as shown in Figure 4, and utilized to simulate the pulsed thrust of thruster. The pair of permanent magnet plates is settled behind the thruster, and the height of Ampere force action spot is set to be the same with the action spot of pulsed thrust of thruster. The distance between the couple of magnets is set 5 mm, and the crest value and duration of current in the conducting wires are controlled by a function generator as shown in Figure 4.

The detailed calibration procedure is described herein.

a. The relationship of Ampere force F and the volts d.c. output X of the function generator is tested by using an electronic balance (Mettler Toledo XS205, minimum mass 10 μg). The relationship can be expressed as:

$$F = A\_{\bullet} \cup B\_{\bullet} X \tag{15}$$

where the coefficients A<sup>0</sup> and B<sup>0</sup> are obtained after the calibration procedure.

b. The calibration devices are settled on the thrust stand with keeping the distance of permanent magnet plates and the relative location between the permanent magnet plates and the conducting wires. And the pendulum is propelled by the Ampere force with duration of t. Therefore, the relationship of PSD signals S and the volts d.c. output X of function generator can be obtained and written as:

$$S = \mathfrak{g}(X, t) \tag{16}$$

A series of experiments are conducted to test the discharge characteristics and the performance parameters, such as impulse bit, and specific impulse. The experiments are conducted in six

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In order to describe the whole process of ablation plasma expansion and ionization, the properties of the plasma at several specific times should be investigated in detail, such as 3.5 ns (the ablation plasma produced), 10.5 ns (the phase explosion finished), 20 ns (the target ablation finished), 60.5 ns (the ablation plasma reaches the wall of the ceramic tube), 100 ns and 200 ns. By solving the gas-dynamical Eq. (8), the plasma velocity, temperature and electron

The spatial distribution of plasma velocity along the centerline of the ceramic tube for different times are presented in Figure 5(a), and the variety of the peak plasma velocity with time is presented in the Figure 5(b). It can be seen from Figure 5(a), the peak plasma velocity appears at the front of the plasma. At 3.5 ns, the plasma has ejected from the target, and the peak velocity is about 2400 m/s. Afterwards, the phase explosion occurs at the target surface, and the ablation products carry out lots of heat from the target to the plasma. Hence the plasma velocity quickly increases, due to the phase explosion and the absorption of the laser energy. Thus at 10.5 ns, the peak plasma velocity increases to 4000 m/s. When the target ablation is finished (at 20 ns), the peak plasma velocity is around 4600 m/s. After finishing the target ablation, the plasma velocity still increases. But the increasing rate of the plasma velocity gradually decrease as shown in Figure 5(b), due to the absence of the absorption of the laser

Figure 5. (a) Distribution of plasma velocity for different times. (b) Variety of the peak velocity with time.

cases, as shown in Table 1.

4. Results and discussion

4.1. Plasma expansion and ionization

number density fraction can be numerically calculated.

energy and the injection of the ablation products.

For the sake of simplification and considering that the pendular period of pendulum is generally longer than 5 s in the experiments, the duration of Ampere force t can be set 1 s by the function generator hereafter. Hence, the expression (16) can be expressed as:

$$S = \mathfrak{g}(X) \tag{17}$$

According to further study, it's indicated that the expression (17) can be simplified as:

$$
\mathcal{S} = \mathcal{A} + \mathcal{B}X \tag{18}
$$

where, the coefficients A and B in expressions (18) could be obtained in the calibration procedures, as shown in Table 1. Besides, according to expression (15), the impulse bit I<sup>b</sup> can be expressed as:

$$I\_b = F\sharp = (A\_b \wedge B\_u X)\sharp \tag{19}$$

c. The relationship of impulse bit and PSD signal S can be obtained as:

$$M\_{\star} = (S - A)B\_0 \, ^i R + A\_0 \tag{20}$$

The uncertainty analysis is important and conducted herein. There are many sources of error for operating this thrust stand which must be identified, then quantified in order to evaluate the accuracy of the impulse bit measurement. It is shown in the expression (20) that the impulse bit is calculated from the voltage values of PSD signals and the coefficients in calibration procedures, A, A0, B and B0. Therefore, the uncertainties in the system data and results can be categorized into two main types. Firstly, the calibration procedures may generate errors for obtaining the coefficients A, A0, B and B0. Secondly, the impulse bit measurement is another source of error.

#### 3.3. Measurement for mass shots

The mass shots are measured for the six cases by using an electronic balance (Mettler Toledo XS205, minimum mass 10 μg). It is apparent that the mass shots with different charged energy for a laser pulse energy of 600 mJ are approximately the same for the first five cases in Table 1, because of the isolation of laser ablation and discharge processes in the thruster. The typical number of pulse-shots to measure the mass shots is 100 times. The mass consumptions of propellants per shot are tested approximately as 15.7 and 7.8 μg for PTFE and aluminum, respectively. It is remarkable that the ablation of ceramic tube and ceramic insulator is much weak and not considered herein.

A series of experiments are conducted to test the discharge characteristics and the performance parameters, such as impulse bit, and specific impulse. The experiments are conducted in six cases, as shown in Table 1.
