The spatial distributions of characteristic parameters for plasma created by hypervelocity impact

Abstract

In order to better describe the spatial distributions of characteristic parameters for plasma generated by hypervelocity impact, a large number of experiments have been performed by using two-stage light gas gun loading system and measurement system of plasma characteristic parameters. Based on experimental results determining the splash process, the expanding process of the plasma cloud ejected is obtained near the impact point. For physical process of oblique collision, the expansion of plasma cloud is approximately ellipsoidal distribution. Based on expanding characteristics of plasma cloud determine the space layout of triple Langmuir probe, characteristic parameters of plasma generated by hypervelocity impact are acquired at the incidence angles of 45 ${}^{\circ}$ and 60 ${}^{\circ}$ and the impact velocities of about 3 km/s. In the paper, the ellipsoidal equations of the plasma cloud generated by collisions are determined in the three-dimensional space, and the spatial distributions of the plasma characteristic parameters are established. According to the geometric distribution established by hypervelocity impact on 2A12 aluminum plate, the rules and average expanding velocity of the plasma cloud are obtained. Furthermore, the average expanding velocity of plasma cloud increase with the decreasing of the distance from the measured point to impact point at the impact velocities of about 3 km/s and the incidence angles of 45 ${}^{\circ}$ and 60 ${}^{\circ}$ , respectively. Meanwhile, the linear relationships about impact velocities and distances from the measured point to the impact point are more stronger at the incidence angle of 60 ${}^{\circ}$ than that at the incidence angle of 45 ${}^{\circ}$ . It is of great significant to further reveal the physical process of the plasma generated by hypervelocity impact.

Keywords

Hypervelocity impact plasma characteristic parameters spatial distribution expanding velocity of the plasma cloud

1. Introduction

When a meteoroid or a meteorite collides with the interstellar surface, the debris clouds ejected contain plasma in the early collision process, which results in a large, short-lived magnetic field. Most of the hypervelocity impact ejected from the interstellar surface contain plasmas. We believes that the debris cloud expands outward at an average speed of 8 km/s at the later stage of the collision, and the magnetic field will increase. The formation and evolution of the transient magnetic field inside the plasma is caused by hypervelocity impact, which covers three stages of penetration, cavity formation and later expansion of the vapor cloud. The theory that hypervelocity collisions produce plasmas and transient magnetic fields may explain the residual magnetic field of the moon’s surface [1, 2, 3, 4]. Pert [5] derived the model of collision plasma generated in his work, then Hood and Vickery pointed out that the decisive significance of the internal electron density and temperature gradient in plasma cloud generated on the laboratory scale [4, 5, 6, 7, 8]. However, the establishment of the characteristic parameter’s distribution for plasma generated by hypervelocity impact is still blank at home and abroad at the different spatial positions in some space region [9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. In order to avoid the influence of too much sensors placed to the experimental results at the same experiment. Spatial distribution models of the maximum electron temperature and the density are established through installing sensors at the different spatial positions based on the large number of similar parameter’s hypervelocity impact experiments, the characteristic parameters of plasma are obtained through experimental data acquisition and MATALB software programming treatment.

2. Experiment

The experiments have been performed on the two-stage light gas gun at the Intense Dynamic Load Research Center of Shenyang Ligong University. The two-stage light gas gun can accelerate the spherical aluminum projectile of 4.8 mm diameter to 7 km/s, and the vacuum capacity of the target chamber can reach 10 Pa. The projectile is a 2A12 aluminum ball with a diameter of 4.8 mm, and the target is 2A12 aluminum plate with length $\times$ width $\times$ thickness $=$ 120 $\times$ 120 $\times$ 20 mm ${}^{3}$ . A total of experiments is 18 sets, when the incident angle (between the projectile trajectory and target plane) is 45 ${}^{\circ}$ , the collision speeds are 3.22 km/s, 3.15 km/s, 2.86 km/s, 3.02 km/s, 3.14 km/s, 2.9 km/s, 2.88 km/s, 3.12 km/s and 2.96 km/s, respectively; when the incident angle of the projectile is 60 ${}^{\circ}$ , the impact velocities are 3.06 km/s, 2.86 km/s, 3.09 km/s, 3.03 km/s, 3.14 km/s, 2.95 km/s, 3.07 km/s, 3.15 km/s and 3.03 km/s, respectively. Figure 1 is the structural scheme of the two-stage light gas gun loading system.

Figure 1.

Structural scheme of the two-stage light gas gun loading system.

3. Diagnostic system

3.1 Diagnostic system of plasma characteristic parameters

The diagnostic system of plasma characteristic parameters mainly includes Triple Langmuir Probe (TLP) [19], diagnostic circuit, oscillograph and DC power supply. The TLP is used to diagnose the electron temperature and density of the plasma. The TLP is fixed above the target, and the TLP is aligned with the impact point. The TLP is made up of 3 single core coaxial cables, which type is SYV50-3. The cable was stripped off the outer skin, shielding net and outer plastic shell. The TLP is made of copper wire with a length of 6 mm and a diameter of 0.28 mm. In the experiments, the DC power supplied by the 18 V and 3 V dry batteries provides DC bias for the TLP. When the detection point does not appear the plasma, the whole system is open, and potential does not change in the four channels of the oscilloscope; when the detection point produces plasma by hypervelocity impact and the plasma density is large enough, the whole system will be in a closed state, the voltage changes of each branch are recorded and stored in a closed circuit by oscilloscope. Figure 1 is a schematic diagram of the diagnostic system circuit for Triple Langmuir Probe.

Figure 2.

Schematic diagram of diagnostic circuit for Triple Langmuir Probe.

3.2 Diagnostic theory of plasma characteristic parameters

According to the principle of Triple Langmuir Probes proposed by Chen and Sekiguchi, the electron temperature Te and electron density $N_{e}$ of plasma produced by hypervelocity collisions are determined. Assuming the plasma generated by hypervelocity impact is in the local equilibrium state in the expanding process, in each local equilibrium plasma, all evenly through the TLP, the electron energy in the plasma is satisfies with Maxwell distribution, the electron temperature Te (eV) of the plasma generated by hypervelocity impact can be obtained by the following formula

$\displaystyle\frac{I_{1}+I_{2}}{I_{1}+I_{3}}=\frac{1-\exp(-\Phi_{d2})}{1-\exp(% -\Phi_{d3})}$ (1) $\displaystyle I_{1}=I_{2}+I_{3}$ (2) $\displaystyle\Phi_{d2}=\frac{eV_{d2}}{kT_{e}}$ (3) $\displaystyle\Phi_{d3}=\frac{eV_{d3}}{kT_{e}}$ (4)

Wherein, $I_{1}$ , $I_{2}$ and $I_{3}$ are the currents flowing through the TLP; $V_{d2}$ and $V_{d3}$ are the applied voltage in the circuit, the corresponding values 3 V and 18 V. The electron density Ne (m ${}^{-3}$ ) of plasma generated by hypervelocity collisions can be obtained by calculating the electron temperature

$\displaystyle I_{i}=\frac{I_{3}-I_{2}\exp(-\Phi_{\Delta v})}{1-\exp(-\Phi_{% \Delta v})}$ (5) $\displaystyle f_{1}(V_{d2})=1.05\times 10^{15}(T_{e})^{-1/2}\left[{\exp(\Phi_{% d2})-1}\right]^{-1}$ (6) $\displaystyle N_{e}=\left[{(M)^{1/2}/S}\right]I_{i}f_{1}(V_{d2})$ (7)

Wherein, $M$ is ion mass, its unit $g$ ; $S$ is an exposed area of a single probe, the unit mm ${}^{2}$ ; $\Delta V=V_{2}-V_{3}$ . Among them, $V_{2}$ and $V_{3}$ can be determined by the four channels of the oscilloscope, the unit of $I_{i}$ is $\mu A$ .

3.3 Establishment of space coordinate system

The impact point as the origin of coordinates of O (0, 0, 0), pointing to the trajectory direction as the positive direction of space coordinate of the Y axis perpendicular to the target plane and direction upward as the positive direction of the Z axis, X axis direction meet the right hand rule. In the experiments, the exposed portion of the TLP is always pointing perpendicularly to the target. The spatial coordinates of the experimental system are shown in Fig. 3.

Figure 3.

Space coordinate system of the experimental system.

4. Experimental results and analysis

4.1 Electron temperature and density under the typical experimental parameters

Based on the diagnostic principle of TLP and Matlab software programmed, the variable curves of the electron temperature and the density for plasma with time are obtained from 2 group typical experiments. The electron temperature and density of the plasma are shown in Figs 4 and 5.

Figure 4.

Variation of electron temperature and density with time.

Figure 5.

Variation of electron temperature and density with time.

As can be seen from Figs 4 and 5, the electron density and temperature of the plasma produced by hypervelocity impact are experienced from the appearing and rising gradually to the peak and then disappearing slowly. At the impact moment, the energy changes rapidly and resulting in partial high temperature. Ionization of some substances in the ejecta results in a plasma cloud, which increases the electron density and temperature of the plasma. We can see from Fig. 5 that the the data was more noiser for the incidence angle of 60 ${}^{\circ}$ than that at the incidence angle of 45 ${}^{\circ}$ because more ejector was ejected from the molten pool and produced Intermittent jet which induced a large disturbance at the TLP at the incidence angle of 60 ${}^{\circ}$ .

4.2 Experimental data processing results

In order to establish the spatial distribution model of the characteristic parameters for the plasma generated by hypervelocity impact, Experiments are carried out by hypervelocity impact on 2A12 aluminum plate at the near impact velocities and incidence angles (trajectory and target plane) of 45 ${}^{\circ}$ and 60 ${}^{\circ}$ , respectively. The maximum electron temperature and density of the plasma are obtained based on the diagnostic theory of plasma characteristic parameter and the Matlab software programming. Table 1 is experimental parameters and corresponding plasma characteristic parameters.

Table 1
Experimental parameters and corresponding characteristic parameters of plasma

Experimental

codes

Impact

angle/(

{}^{\circ}

)

Impact

velocity/

(km/s)

Distance from

trigger to impact

point/(mm)

Coordinate of the

TLP (X, Y, Z)/

(mm)

Maximum

electron

temperature/(eV)

Maximum

electron

density/(m

{}^{-3}

)

No.1

3.22

360

(20, 32, 25)

3.95

9.2

\times

{}^{15}

No.2

3.14

365

(30, 25, 25)

4.0

11.1

\times

{}^{15}

No.3

3.02

345

(35, 22, 25)

4.1

10.2

\times

{}^{15}

No.4

2.86

265

(35, 25, 30)

4.2

10.9

\times

{}^{15}

No.5

2.9

265

(45, 35, 30)

4.0

9.5

\times

{}^{15}

No.6

2.88

300

(20, 60, 30)

3.95

9.05

\times

{}^{15}

No.7

3.12

290

(45, 60, 50)

3.68

6.3

\times

{}^{15}

No.8

2.96

280

(42, 65, 50)

3.7

6.67

\times

{}^{15}

No.9

3.15

280

(30, 49, 50)

3.4

5.8

\times

{}^{15}

No.10

2.86

365

(35, 39, 25)

4.2

\times

{}^{15}

No.11

3.09

360

(33, 46, 25)

4.0

10.2

\times

{}^{15}

No.12

3.03

355

(37, 40, 25)

4.0

10.1

\times

{}^{15}

No.13

3.14

360

(47, 36, 41)

3.84

9.4

\times

{}^{15}

No.14

2.95

365

(35, 50, 40)

3.87

8.1

\times

{}^{15}

No.15

3.07

360

(35, 70, 40)

3.7

6.4

\times

{}^{15}

No.16

3.15

315

(44, 42, 50)

3.5

6.2

\times

{}^{15}

No.17

3.03

360

(35, 30, 50)

3.88

9.9

\times

{}^{15}

No.18

3.06

360

(

-

50, 43, 50)

3.78

5.2

\times

{}^{15}

4.3 Spatial distribution model of plasma characteristic parameters

4.3.1 The spatial distributions of electron temperature and density at the incidence angle of 45 ${}^{\circ}$

Spatial distribution model of maximum electron temperature and density are constructed based on experimental original data acquired by hypervelocity impact on 2A12 aluminum plate combining with TLP diagnostic system and Matlab software programming from experimental data of Table 1 at the incidence angle of 45 ${}^{\circ}$ . Based on spatial position’s coordinate of TLP and maximum electron temperature and density of plasma obtained, and impact point (coordinate origin) as ellipsoidal center to fit three part ellipsoidal stratifications, the spatial distribution model of the plasma characteristic parameters are obtained by processing the experimental data of plasma created by hypervelocity impact on 2A12 aluminum plate. Figure 6 is the distribution model of the plasma characteristic parameters.

Figure 6.

(a) Spatial geometric model of plasma characteristic parameters; (b) Plasma characteristic parameters of 1/4 space at the positive direction of the coordinate axis.

In order to observe and describe the spatial characteristics of the electron temperature and density of the plasma, the 1/4 ellipsoid in the positive direction of the spatial coordinate axis is selected, and Fig. 6a is rotated to obtain Fig. 6b. The maximum electron temperature Te and the maximum electron density Ne in the Cartesian coordinate system can be obtained by experimental data from the TLP in Table 1, and the units are in agreement with the units of each parameters in Fig. 6b. The ellipsoidal equations are obtained by fitting data processing results from the inner to the outer layers of the ellipsoid

$\displaystyle\text{Inner layer}\frac{x^{2}}{58^{2}}+\frac{y^{2}}{52^{2}}+\frac% {z^{2}}{47^{2}}=1$ (8) $\displaystyle\text{Middle layer}\frac{x^{2}}{65^{2}}+\frac{y^{2}}{79^{2}}+% \frac{z^{2}}{53^{2}}=1$ (9) $\displaystyle\text{Outer layer}\frac{x^{2}}{75^{2}}+\frac{y^{2}}{116^{2}}+% \frac{z^{2}}{82^{2}}=1$ (10)

According to Fig. 6b, we can know that the maximum electron temperatures and densities are near the same at the 3 measured points of the same ellipsoidal surface, also verified the approximate ellipsoidal expansion of the plasma cloud outerward near the impact point at the incidence angle of 45 ${}^{\circ}$ and the impact velocity about 3.0 km/s during hypervelocity impact on 2A12 aluminum plate. The plasma cloud expand from the inner to the outer away impact point, the relationships between maximum electron temperature and density and the distance from each measured point to impact point can be obtained based on the fitting of maximum electron temperatures and maximum electron densities, and the error bars are 5 percent, respectively. Figure 7a is the variable curve of the maximum electron temperature with the distance from the measured point to the impact point. Figure 7b is the relationship between the maximum electron density and the distance from the measured point to the impact point.

Figure 7.

(a) Variable curve of the maximum electron temperature with distance from measured point to impact point; (b) Variable curve of the maximum electron density with distance from measured point to impact point.

The fitting relationship between the maximum electron temperature and the distance from the measured point to the impact point can be expressed as

$\displaystyle T_{e}=\frac{0.4886^{\pm 0.012}}{1+e^{(d-72.0239^{\pm 2.2})/3.837% 4}}+3.5915^{\pm 0.275}$ (11)

Wherein, $T_{e}$ is the maximum electron temperature; $d$ is the distance from the measured point to the impact point. The fitting relationship between the maximum electron density and the distance from the measured point to the impact point can be expressed as

$\displaystyle N_{e}=\frac{5.165^{\pm 0.212}\times 10^{15}}{1+e^{(d-70.6084^{% \pm 2.62})/7.6484}}+5.895^{\pm 0.32}\times 10^{15}$ (12)

Wherein, $N_{e}$ is the maximum electron density, $d$ is the distance from the measured point to the impact point. As illustrated in Fig. 7, the maximum electron temperature and maximum electron density decrease with the plasma cloud expanding outward. The maximum electron temperature and maximum electron density have a similar fitting relationship, which show that the two case have a similar expanding type from the internal to the external layer of the ellipsoid.

4.3.2 The spatial distributions of electron temperature and density at the incidence angle of 60

{}^{\circ}

Spatial distribution model of maximum electron temperature and density are constructed based on experimental raw data acquired by hypervelocity impact on 2A12 aluminum plate combining with TLP diagnostic system and Matlab software programming based on the experimental data of Fig. 10 at the incidence angle of 60 ${}^{\circ}$ and the impact velocity. Figure 8 is the spatial distribution model of the plasma characteristic parameters.

Figure 8.

(a) Spatial geometric model of plasma characteristic parameters; (b) Plasma characteristic parameters of 1/4 space at the positive direction of the coordinate axis.

In order to better observe and describe the spatial distribution characteristics of the electron temperature and density, the 1/4 ellipsoid in the positive direction of the space coordinate axis is selected, and Fig. 8a is rotated to obtain Fig. 8b. The data in Fig. 8b are the maximum electron temperature Te and the maximum electron density Ne in the Cartesian coordinate system obtained by the TLP, and the units are in agreement with the units of each parameters in Fig. 8b. The ellipsoidal equations are obtained by fitting from the inner to the outer layers of the ellipsoid

$\displaystyle\text{Inner layer}\frac{x^{2}}{63^{2}}+\frac{y^{2}}{64^{2}}+\frac% {z^{2}}{53^{2}}=1$ (13) $\displaystyle\text{Middle layer}\frac{x^{2}}{75^{2}}+\frac{y^{2}}{82^{2}}+% \frac{z^{2}}{62^{2}}=1$ (14) $\displaystyle\text{Outer layer}\frac{x^{2}}{86^{2}}+\frac{y^{2}}{97^{2}}+\frac% {z^{2}}{72^{2}}=1$ (15)

According to Fig. 8b, we can know that the maximum electron temperatures and densities are near the same at the 3 detecting points of the same ellipsoidal surface, also verified the approximate ellipsoidal expansion of the plasma cloud outerward near the impact point at the incidence angle of 60 ${}^{\circ}$ and the impact velocity about 3.0 km/s during hypervelocity impact on 2A12 aluminum plate.

The plasma cloud expand from the inner to the outer layer away impact point, the relationships between maximum electron temperature, density and the distance from each measured point to a impact point can be obtained based on the fitting of maximum electron temperatures and maximum electron densities, and the error bar are 5 percent, respectively. Figure 9a is the variable curve of the maximum electron temperature with the distance from the measured point to the impact point. Figure 9b is the relationship between the maximum electron density and the distance from the measured point to the impact point.

Figure 9.

(a) Variable curve of the maximum electron temperature with distance from the measured point to impact point; (b) Variable curve of the maximum electron density with distance from measured point to impact point.

The fitting relationship between the maximum electron temperature and the distance from the measured point to the impact point can be expressed as

$\displaystyle T_{e}=\frac{0.5105^{\pm 0.08}}{1+e^{(d-66.8427^{\pm 1.98})/4.890% 1}}+3.6642^{\pm 0.23}$ (16)

$\displaystyle N_{e}=\frac{4.2276^{\pm 0.117}\times 10^{15}}{1+e^{(d-73.4038^{% \pm 0.52})/2.1884}}+5.8474^{\pm 0.44}\times 10^{15}$ (17)

Wherein, $N_{e}$ is the maximum electron density, $d$ is the distance from the measured point to the impact point. As illustrated in Fig. 8, the maximum electron temperature and maximum electron density decrease with the plasma cloud expanding outward. The maximum electron temperature and maximum electron density have a trend downward.

4.4 The expanding velocity of the plasma cloud

It can be seen from Fig. 9 that the plasma cloud is expanding from inner layer to outer layer, and the expansion of the plasma cloud among layers is very uneven, which shows that the plasma generated by hypervelocity impact has uneven distribution and a large fluctuation. Therefore, the average expanding velocity of the plasma cloud (the average velocity from the impact point to measured point ) is used to describe the expanding process of the plasma.

Based on the experimental original data and the mean expanding velocity of the plasma cloud, the mean expanding velocity of the plasma cloud as shown in Table 1 can be obtained. The curve of the average expanding velocity of the plasma cloud with the distance between the measured point to the impact point is shown in Fig. 10, which the collision speeds and incidence angles are about 3.0 km/s and 45 ${}^{\circ}$ , respectively.

Figure 10.

Variable curve of the average expanding velocities of the plasma cloud with distance from measured point to impact point at the incidence of 45 ${}^{\circ}$ .

The average expanding velocity of the plasma cloud is different corresponding to the distance between the different measured points and the impact point. The average expanding velocity of the plasma cloud decreases with the increasing of the distance between the measured point and the impact point. The fitting relationship between the average expanding velocity of the plasma cloud with the distance from the measured point and the impact point can be expressed as

$\displaystyle v_{p}=-0.05234^{\pm 0.0037}d+8.31704^{\pm 0.28}$ (18)

Wherein, $v_{p}$ is the average expanding velocity of the plasma cloud; $d$ is the distance between the measured point and the impact point.

According to Fig. 10, one can see that the average expanding velocity of plasma cloud increase with the decreasing of the distance from the measured point to impact point at the impact velocity of about 3 km/s and the incidence angle of 45 ${}^{\circ}$ when the distances between the measured point and the impact point are from 46.4 mm to 92.1 mm; Meanwhile, average expanding velocities of plasma cloud are between 3.94 km/s and 5.95 km/s. Figure 11 is variable curve of the average expanding velocity of the plasma cloud with distance from measured point to impact point at the incidence angles of 60 ${}^{\circ}$ , respectively.

Figure 11.

Variable curve of the average expanding velocity of the plasma cloud with distance from measured point to impact point at the incidence angles of 45 ${}^{\circ}$ .

The fitting relationship between the average expanding velocity of the plasma cloud with the distance from the measured point to the impact point can be expressed as

$\displaystyle v_{p}=-0.06856^{\pm 0.0021}d+9.95086^{\pm 0.27}$ (19)

Whierein, $v_{p}$ is the average expanding velocity of the plasma cloud; $d$ is the distance between the measured point and the impact point.

According to Fig. 11, one can know that the average expanding velocity of plasma cloud increase with the decreasing of the distance from the measured point to impact point at the impact velocity of about 3 km/s and the incidence angle of 60 ${}^{\circ}$ when the distances between the measured point and the impact point are from 59.3 mm to 87.9 mm; Meanwhile, the average expanding velocities of plasma cloud are between 3.92 km/s and 6.05 km/s.

5. Conclusion

In the paper, Experiments have been performed by hypervelocity impact on 2A12 aluminum plate combining with the different spatial layouts of Triple Langmuir Probe at the impact velocities of about 3 km/s and the incidence angles of 45 ${}^{\circ}$ and 60 ${}^{\circ}$ , respectively. Draw the following conclusions:

The ellipsoidal equations of the plasma cloud in three-dimensional space coordinate are determined by the Triple Langmuir Probe diagnostic system and the different space coordinates of the TLP combining with the information of the maximum electron temperature and density of plasma generated by hypervelocity impact on 2A12 aluminum target;

The spatial distribution models of the maximum electron temperature and density for plasma created by hypervelocity impact on 2A12 aluminum plate have been established;

The average expanding velocity of plasma cloud increase with the decreasing of the distance from the measured point to impact point at the impact velocity of about 3 km/s and the incidence angle of 45 ${}^{\circ}$ when the distances between the measured point and the impact point are from 46.4 mm to 92.1 mm; At the same time, average expanding velocities of plasma cloud are between 3.94 km/s and 5.95 km/s;

The average expanding velocity of plasma cloud increase with the decreasing of the distance from the measured point to impact point at the impact velocity of about 3 km/s and the incidence angle of 60 ${}^{\circ}$ when the distances between the measured point and the impact point are from 59.3 mm to 87.9 mm; Meanwhile, average expanding velocities of plasma cloud are between 3.92 km/s and 6.05 km/s.

Footnotes

Acknowledgments

Supported by National Natural Science Foundation of China (Grant Nos. 11472178, 10972145, 11272218); supported by Program for Liaoning Excellent Talents in University (No. LR2013008); supported by Open foundation of the State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology (Grant No.KFJJ18-04M).

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The spatial distributions of characteristic parameters for plasma created by hypervelocity impact

Abstract

Keywords

1. Introduction

2. Experiment

3.1 Diagnostic system of plasma characteristic parameters

4.1 Electron temperature and density under the typical experimental parameters

Table 1 Experimental parameters and corresponding characteristic parameters of plasma

4.3.1 The spatial distributions of electron temperature and density at the incidence angle of 45 ∘

Footnotes

Acknowledgments

References

Table 1
Experimental parameters and corresponding characteristic parameters of plasma

4.3.1 The spatial distributions of electron temperature and density at the incidence angle of 45 ${}^{\circ}$