4.1. Plasma expansion and ionization

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 number density fraction can be numerically calculated.

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 energy and the injection of the ablation products.

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

The spatial distribution of plasma temperature along the centerline of the ceramic tube for different times are presented in Figure 6(a). The variety of peak plasma temperature with time is presented in Figure 6(b). As can be seen in Figure 6(a), there are two peaks of the plasma temperature appears nearby the target surface (T1) and at the front of the plasma (T2). T1 is due to the high-temperature ablation products ejection from the target to the plasma. T2 is because of the plasma absorption of laser energy through IB absorption, which causes the plasma temperature to increase. At 3.5 ns, only T1 exists and equals to 4500 K, due to the injection of high-temperature ablation products. However, afterwards, both T1 and T2 appear in the figure. The T1 gradually increases to about 5700 K at 10.5 ns, and then decreases to below 2000 K at 200 ns. We can also conclude from Figure 6(b), the variation tendency of T1 is consistent with the target temperature. The T1 decreases after 10.5 ns. However, the T2 sharply increases during the laser pulse (from 3.5 to 20 ns), and then nearly keep constant after finishing the laser pulse (20 ns). Thus at 200 ns, only T2 exists in the figure. What is coincident, the T1 equals to T2 at 15 ns, therefore the T1 is bigger than T2 before 15 ns and smaller than T2 after 15 ns.

The spatial distribution of plasma electron number density fraction (η) along the centerline of the ceramic tube for different times are presented in Figure 7(a). The variety of the fraction (ψ) of ionization area to the whole ceramic tube area with time is presented in Figure 7(b). As it can be seen in Figure 7(a), the ionization region mainly distributes at the front of the plasma, which is similar to the plasma velocity and temperature. The η increases during the laser pulse, and at 20 ns, the peak η approaches 0.5, which means the plasma is fully ionized at this region. Afterwards, the η keep constant at 0.5, but the area of the fully ionized region continuously increases. However, only primary ionization occurs in the plasma, due to the equilibrium relations of and . We can also conclude from the Figure 7(b), the ψ increases faster during the laser pulse, from 1% at 3.5 ns to 3% at 20 ns. Afterwards, the increasing rate of the ψ gradually decreases, at 200 ns, the ψ approaches 6%.

4.2. Thrust performances

The impulse bits and discharge currents were measured with different parameters d1 and d2. Temporal variations of discharge current between the electrodes for charged voltage conditions from about 300 to 2000 V and a laser pulse energy of 600 mJ are shown in Figure 8

Figure 7. (a) Distribution of plasma electron number density fraction (η) for different times. (b) Variation of the fraction

Plasma Generation and Application in a Laser Ablation Pulsed Plasma Thruster

http://dx.doi.org/10.5772/intechopen.77511

201

It is shown in Figure 8 that the higher the charged energy, the higher the discharge current being achieved. In the case I, a maximal charged energy is 25.2 J, d1 = 20 mm, d2 = 10 mm and the propellant is aluminum. It is shown that the peak value of discharge current under the charged voltage of 2050 V is more than 20 kA. And it is proven that discharge current can be observed under very low charged voltage conditions (~316 V), in which case a discharge current raises up to 2.7 kA at 1.1 μs. Compared between Figure 8(a) and (b), it can be concluded that the peak value of discharge current decrease as d1 increasing for the situation of same charged voltage. Compared between Figure 8(b)–(d), it can be concluded that the peak value of discharge current reaches maximum for the situation of d1 = 2d2, which means the

The specific impulse and thrust efficiency could be calculated from the impulse bits and mass shots tested for the six cases. The curves of specific impulse for each working condition are illustrated as shown in Figure 9. In addition, the thrust efficiency of the thruster is defined as:

where Etotal is the total energy imported by the thruster, consisting of the single laser energy and the charged energy of capacitors, i.e., Etotal = Elaser + Echarge. Ib represents the impulse bit, m is the mass ablated per shot and v is the mean velocity of plasma. And the factor 103 is required in the conversion of units. The thrust efficiency η was calculated and listed in Figure 10.

ð21Þ

respectively. The impulse bits in different cases are shown in Figure 9.

propellant is placed in the middle of the electrodes.

(ψ) of ionization area to the whole ceramic tube area with time.

Figure 6. (a) Distribution of plasma temperature for different times. (b) Variety of peak temperature with time.

Figure 7. (a) Distribution of plasma electron number density fraction (η) for different times. (b) Variation of the fraction (ψ) of ionization area to the whole ceramic tube area with time.

#### 4.2. Thrust performances

The spatial distribution of plasma temperature along the centerline of the ceramic tube for different times are presented in Figure 6(a). The variety of peak plasma temperature with time is presented in Figure 6(b). As can be seen in Figure 6(a), there are two peaks of the plasma temperature appears nearby the target surface (T1) and at the front of the plasma (T2). T1 is due to the high-temperature ablation products ejection from the target to the plasma. T2 is because of the plasma absorption of laser energy through IB absorption, which causes the plasma temperature to increase. At 3.5 ns, only T1 exists and equals to 4500 K, due to the injection of high-temperature ablation products. However, afterwards, both T1 and T2 appear in the figure. The T1 gradually increases to about 5700 K at 10.5 ns, and then decreases to below 2000 K at 200 ns. We can also conclude from Figure 6(b), the variation tendency of T1 is consistent with the target temperature. The T1 decreases after 10.5 ns. However, the T2 sharply increases during the laser pulse (from 3.5 to 20 ns), and then nearly keep constant after finishing the laser pulse (20 ns). Thus at 200 ns, only T2 exists in the figure. What is coincident, the T1 equals to T2 at 15 ns, therefore the T1 is bigger than T2

The spatial distribution of plasma electron number density fraction (η) along the centerline of the ceramic tube for different times are presented in Figure 7(a). The variety of the fraction (ψ) of ionization area to the whole ceramic tube area with time is presented in Figure 7(b). As it can be seen in Figure 7(a), the ionization region mainly distributes at the front of the plasma, which is similar to the plasma velocity and temperature. The η increases during the laser pulse, and at 20 ns, the peak η approaches 0.5, which means the plasma is fully ionized at this region. Afterwards, the η keep constant at 0.5, but the area of the fully ionized region continuously increases. However, only primary ionization occurs in the plasma, due to the equilibrium relations of and . We can also conclude from the Figure 7(b), the ψ increases faster during the laser pulse, from 1% at 3.5 ns to 3% at 20 ns. Afterwards, the increasing rate of the ψ gradually decreases, at 200 ns, the ψ approaches 6%.

Figure 6. (a) Distribution of plasma temperature for different times. (b) Variety of peak temperature with time.

before 15 ns and smaller than T2 after 15 ns.

200 Plasma Science and Technology - Basic Fundamentals and Modern Applications

The impulse bits and discharge currents were measured with different parameters d1 and d2. Temporal variations of discharge current between the electrodes for charged voltage conditions from about 300 to 2000 V and a laser pulse energy of 600 mJ are shown in Figure 8 respectively. The impulse bits in different cases are shown in Figure 9.

It is shown in Figure 8 that the higher the charged energy, the higher the discharge current being achieved. In the case I, a maximal charged energy is 25.2 J, d1 = 20 mm, d2 = 10 mm and the propellant is aluminum. It is shown that the peak value of discharge current under the charged voltage of 2050 V is more than 20 kA. And it is proven that discharge current can be observed under very low charged voltage conditions (~316 V), in which case a discharge current raises up to 2.7 kA at 1.1 μs. Compared between Figure 8(a) and (b), it can be concluded that the peak value of discharge current decrease as d1 increasing for the situation of same charged voltage. Compared between Figure 8(b)–(d), it can be concluded that the peak value of discharge current reaches maximum for the situation of d1 = 2d2, which means the propellant is placed in the middle of the electrodes.

The specific impulse and thrust efficiency could be calculated from the impulse bits and mass shots tested for the six cases. The curves of specific impulse for each working condition are illustrated as shown in Figure 9. In addition, the thrust efficiency of the thruster is defined as:

$$
\eta = E\_{\text{kin-sci}} \; 'E\_{\text{a} \sim \text{d}} = 10^3 \; I\_{\text{b}}^2 \; ' \left( \Omega m E\_{\text{s} \text{an} \text{l}} \right) \tag{21}
$$

where Etotal is the total energy imported by the thruster, consisting of the single laser energy and the charged energy of capacitors, i.e., Etotal = Elaser + Echarge. Ib represents the impulse bit, m is the mass ablated per shot and v is the mean velocity of plasma. And the factor 103 is required in the conversion of units. The thrust efficiency η was calculated and listed in Figure 10.

Figure 8. Discharge current between electrodes with different structural parameters: (a) case I, (b) case II, (c) case III and (d) case IV.

Figure 9. Variations of impulse bit with charged energy.

Plasma Generation and Application in a Laser Ablation Pulsed Plasma Thruster

http://dx.doi.org/10.5772/intechopen.77511

203

Figure 10. Variations of specific impulse with charged energy.

The impulse bits and specific impulses of thruster increase with the charged energy of capacitors, as shown in Figures 9 and 10. However, the thrust efficiency in case V decreases with the increment of charged energy in the range of 6–10 J, as shown in Figure 11. The rate of change of specific impulse or the thrust efficiency to charged energy is much smaller than at the higher energy levels.

Maximal specific impulse, impulse bit and thrust efficiency are achieved with a charged energy of above 25 J for all cases, as shown in Figures 9–11. For the case III, with a charged energy 25 J and the use of metal aluminum, a maximal impulse bit of 600 μNs, a specific impulse of approximate 8000 s and thrust efficiency of about 90% are obtained.

In addition, when the charged voltage is decreased to 0 V, the status can be called as the pure laser propulsion mode. And status with a charged voltage above zero is called as electromagnetic acceleration mode. The left ends of curves in Figure 6 represent the impulse bit with low charged energy levels and that the discharge processes are weak, and the impulse bits equal approximately with the impulse bits in pure laser propulsion modes.

Figure 9. Variations of impulse bit with charged energy.

The impulse bits and specific impulses of thruster increase with the charged energy of capacitors, as shown in Figures 9 and 10. However, the thrust efficiency in case V decreases with the increment of charged energy in the range of 6–10 J, as shown in Figure 11. The rate of change of specific impulse or the thrust efficiency to charged energy is much smaller than at the higher

Figure 8. Discharge current between electrodes with different structural parameters: (a) case I, (b) case II, (c) case III and

Maximal specific impulse, impulse bit and thrust efficiency are achieved with a charged energy of above 25 J for all cases, as shown in Figures 9–11. For the case III, with a charged energy 25 J and the use of metal aluminum, a maximal impulse bit of 600 μNs, a specific impulse of appro-

In addition, when the charged voltage is decreased to 0 V, the status can be called as the pure laser propulsion mode. And status with a charged voltage above zero is called as electromagnetic acceleration mode. The left ends of curves in Figure 6 represent the impulse bit with low charged energy levels and that the discharge processes are weak, and the impulse bits equal approximately with the impulse bits in pure laser propulsion modes.

ximate 8000 s and thrust efficiency of about 90% are obtained.

202 Plasma Science and Technology - Basic Fundamentals and Modern Applications

energy levels.

(d) case IV.

Figure 10. Variations of specific impulse with charged energy.

2. There are two peaks of the plasma temperature appear in the plasma along the centerline of the ceramic tube. The peak temperature nearby the target is due to the injection of the high-temperature ablation products. Hence its variation tendency is consistent with the target temperature. The peak temperature exist at front of the plasma is because of the IB absorption of the laser energy. Hence it increases during the laser pulse, and keep constant

Plasma Generation and Application in a Laser Ablation Pulsed Plasma Thruster

http://dx.doi.org/10.5772/intechopen.77511

205

3. The plasma electron number density fraction increases during the laser pulse, and approaches 0.5 when the laser pulse finished, which means fully ionized in this region. After finishing the laser pulse, the plasma electron number density fraction keep constant, but the

4. The thrust performance is proven to be improved by the electromagnetic acceleration. In contrast with the pure laser propulsion mode, the thrust performance of electromagnetic

5. The impulse bit and specific impulse increased with the charged energy. The optimal thrust performance of the thruster in experiments exists in large charged energy modes. With the charged energy 25 J and the use of metal aluminum, a maximal impulse bit of 600 μNs, a specific impulse of approximate 8000 s and thrust efficiency of about 90% are obtained. For the PTFE propellant, a maximal impulse bit of about 350 μNs, a specific

The authors would like to thank National Natural Science Foundation of China for the finan-

impulse of about 2400 s, and thrust efficiency of about 16% are obtained.

cial assistance provided under the grant numbers 11772354 for this work.

\*Address all correspondence to: jjwu@nudt.edu.cn

DOI: 10.1016/j.actaastro.2008.03.018

Jianjun Wu\*, Yu Zhang, Yuqiang Cheng, Qiang Huang, Jian Li and Xiaobin Zhu

College of Aerospace Science and Engineering, National University of Defense Technology,

[1] Pozwolski A. Electromagnetic propulsion of satellites. Acta Astronautica. 2008;63:575-577.

after finishing the laser pulse.

acceleration modes is much better.

Acknowledgements

Author details

Changsha, Hunan, China

References

area of the fully ionized region continuously increases.

Figure 11. Variations of thrust efficiency with charged energy.

As shown in Figure 9, the impulse bit in pure laser propulsion mode can be estimated as 10–30 μNs with an approximate specific impulse of 100–300 s and thrust efficiency of 1–4%. In contrast with the pure laser propulsion mode, the thrust performance in electromagnetic acceleration mode is much better. It is apparent that the discharge processes do enhance and accelerate the laser plasma. And the thrust performance is proven to be improved by the electromagnetic acceleration.
