**4.1 Behaviors of total electric field (**j j *E* **) during plasma evolution**

**Figure 5(a)** and **(b)** shows the evolution of the radial profiles of the total electric field taken on the different axial locations for two time instances, 3 μs and 20 μs, after the MW launch. The radial profiles show the total electric field intensity to be more near the MW launching port (z = �40 mm). As one moves toward the extraction (z = �60 mm), its values is decreased because of the plasma shielding effect.

A sharp change in the E-field is shown in **Figure 5(a)** at the time, t = �3 μs near the 2.45 GHz ECR surface (r ≈ 23 mm) for the planes, z = �20 mm. The strong inhomogeneity in the E-field implies the absorption of the MW power at the same locations [27]. The power absorption location is also dependent on the magnetic field profile as well within the cylindrical cavity. Another figure, **Figure 5(b)** shows the radial E-field pattern across the different planes for time, t = 20 μs. The inhomogeneous part of the E-field profile looks similar to **Figure 5(a)** for the case of z = �20 mm plane. But the intensity of the E-field is being reduced with time due to the plasma shielding. One can observe that the inhomogeneous part of the E-field is shifted toward the off-ECR regime (r ≈ 28 mm) from the ECR surface with the increase of time. Therefore, the power absorption region is being shifted from the ECR zone to the off-ECR zone. This effect is visible in the power deposition location throughout the cylindrical cavity in **Figure 6**. **Figure 5(a–d)** shows the corresponding shifting of the power deposition location from the ECR zone to the off-ECR zone or UHR zone with time. As the plasma reaches steady state during the time, t = 20 μs, the evolution of the plasma density and temperature is shown in **Figure 7**.

#### **Figure 5.**

*(a) Total electric field (*j j E *) magnitude during gas ignition time of* �*3 μs, (b) total electric field (*j j E *) magnitude during gas ignition time of* �*20 μs.*

*Evolution of Microwave Electric Field on Power Coupling to Plasma during Ignition Phase DOI: http://dx.doi.org/10.5772/intechopen.92011*

## **4.2 Time evolution of plasma with power deposition**

evolution of the different components of the electric fields and correspondingly the plasma parameters is shown in the results and discussion section given below to study their effects on the plasma parameters. To understand the resonance zone in the plasma chamber, the required magnetic field contours are shown in **Figure 4**.

This section of the chapter shows the temporal behavior of the electric fields, power deposition and the corresponding variation of plasma density and hot electron temperature from the start of MW launch to the steady state condition.

**Figure 5(a)** and **(b)** shows the evolution of the radial profiles of the total electric field taken on the different axial locations for two time instances, 3 μs and 20 μs, after the MW launch. The radial profiles show the total electric field intensity to be more near the MW launching port (z = �40 mm). As one moves toward the extraction (z = �60 mm), its values is decreased because of the plasma shielding

A sharp change in the E-field is shown in **Figure 5(a)** at the time, t = �3 μs near

the 2.45 GHz ECR surface (r ≈ 23 mm) for the planes, z = �20 mm. The strong inhomogeneity in the E-field implies the absorption of the MW power at the same locations [27]. The power absorption location is also dependent on the magnetic field profile as well within the cylindrical cavity. Another figure, **Figure 5(b)** shows the radial E-field pattern across the different planes for time, t = 20 μs. The inhomogeneous part of the E-field profile looks similar to **Figure 5(a)** for the case of z = �20 mm plane. But the intensity of the E-field is being reduced with time due to the plasma shielding. One can observe that the inhomogeneous part of the E-field is shifted toward the off-ECR regime (r ≈ 28 mm) from the ECR surface with the increase of time. Therefore, the power absorption region is being shifted from the ECR zone to the off-ECR zone. This effect is visible in the power deposition location

throughout the cylindrical cavity in **Figure 6**. **Figure 5(a–d)** shows the

corresponding shifting of the power deposition location from the ECR zone to the off-ECR zone or UHR zone with time. As the plasma reaches steady state during the time, t = 20 μs, the evolution of the plasma density and temperature is shown in

*(a) Total electric field (*j j E *) magnitude during gas ignition time of* �*3 μs, (b) total electric field (*j j E *)*

**4.1 Behaviors of total electric field (**j j *E* **) during plasma evolution**

**4. Results and discussion**

*Selected Topics in Plasma Physics*

effect.

**Figure 7**.

**Figure 5.**

**52**

*magnitude during gas ignition time of* �*20 μs.*

**Figure 6a** shows that the MW power is being deposited exactly on the ECR (0.0875 T) surface corresponding to the launch MW frequency of 2.45 GHz when the plasma density is low. But as time passes (see **Figure 6b–d**), the power deposition location gets shifted in the off-ECR or upper hybrid resonance (UHR) regime. The UHR zone is a region where the two conditions *ne* < *ncrit* and B < BECR are satisfied [26–28]. The term *ncrit* represents the critical density for the MW frequency, 2.45 GHz that is 7*:*<sup>4</sup> <sup>10</sup><sup>16</sup> <sup>m</sup>3. If one can compare **Figures 6(c)** and **7(a)**, one can visualize that the plasma density (1.3 <sup>10</sup><sup>17</sup> <sup>m</sup><sup>3</sup> ) crosses the critical density from 2.5 μs onwards and the plasma density that is above the critical density is denoted as overdense plasma. So as the overdense plasma is achieved, the electrons get accelerated by less amount of MW energy on the ECR surface. Correspondingly, the plasma bulk temperature increases from the start of MW launch (t = 0 s) to the instant of 630 ns. It is evident from **Figure 7a** that the plasma bulk electron temperature increases and becomes steady near a value of 80 eV. Then the plasma bulk temperature decreases in a faster way with further increase of time. Hence, one can conclude that heating through ECR process is being ceased to occur with the further increase in time. The causes to increase the absorbed power density is expected to be highest (<sup>5</sup> <sup>10</sup><sup>7</sup> W/m3 ) on the ECR surface during the time, t = 630 ns.

#### **Figure 6.**

*Power deposition density at different time steps for 70 W of absorbed power. (a) t = 10 ns, peak power density is 6.6 <sup>10</sup><sup>4</sup> W/m3 , (b) t = 630 ns, peak power density is 1.43 107 W/m<sup>3</sup> , (c) t = 2.5 μs, peak power density is 5.12 <sup>10</sup><sup>6</sup> W/m<sup>3</sup> and (d) t = <sup>40</sup> <sup>μ</sup>s, peak power density is 1.67 107 W/m<sup>3</sup> .*

Correspondingly, the plasma density also reaches above the critical density. The

decrease in the plasma bulk temperature and the corresponding increase of the plasma density even above the critical density are attributed to be occurring from the off-ECR or ES surface wave heating mechanisms [29, 30]. In other words, although the plasma density is approaching steady state (**Figure 7a**), the tempera-

*Evolution of Microwave Electric Field on Power Coupling to Plasma during Ignition Phase*

To confirm the off-resonance or electrostatic heating methods as discussed above, the evolution of the MW electric field and the electrostatic electric field is shown simultaneously in **Figure 7(b)**. The radial distribution of the two types of the

From the above-mentioned results (**Figures 6** and **7**), it can be commented that the power is absorbed by the ECR mechanism especially in the plasma condition where the density is below (underdense plasma) the critical density and slightly above the critical density (overdense plasma). If one notices the plasma parameters for the underdense conditions, one can observe that the density remains below the critical density from the time, t = t = 45 ns to t = 110 ns*.* In this case, the plasma electrons are magnetized and hence are following the magnetic field lines. The field free zones that are located near (r, z) = (0, 0) are being filled by the plasma particles because of the diffusion processes. Due to the ECR heating, the electron temperature is being increased in the field free zones in the underdense plasma situation, t < 110 ns. As the magnetic field lines are stronger (B 2300–2600 G) near the radial locations of the cavity, i.e., in the gaps of the two pairs of ring magnets, the plasma bulk electron temperature exhibits a sharp gradient in those regions. The maximum plasma bulk electron temperature achievable is 85 eV that occurs during the time, t = 280 ns*.* The high energy part of the plasma bulk electrons is being concentrated

It is observed that the plasma bulk electron temperature increases in the radial direction at the regions mainly in between the two pairs of the ring magnets with the increase in time from t = 280 ns to 730 ns [22]. Therefore, it can be summarized that with the increase in plasma density (or time, t = 45 ns to t = 280 ns) from underdense to overdense state, the plasma bulk temperature is increased by an amount of 80 eV mainly in the radial direction near the region, 24 mm < r < 40 mm, 25 mm < z < 25 mm. This is because the ECR surfaces lie in those regions. The continuous heating through ECR in this location causes the high energy part of the plasma electron temperature to be concentrated on the same location

The anisotropic behavior of the plasma bulk electron temperature even in the overdense plasma signifies the ECR heating [31, 32]. With further increase of time after the MW launch, i.e., near t = 2000 ns, the plasma bulk temperature (Te) is

completely in the same gap as mentioned before during this time.

even in the overdense plasma state during the time t = 730 ns.

electric field is given in that figure for two discrete time instants and the corresponding plasma densities. One can observe that the MW electric field is significant throughout the cavity and is more than the electrostatic electric field for the time, t = 500 ns. For another instance, t = 2 μs, the electrostatic electric field becomes more than the MW electric field throughout the cavity. The electrostatic field is even more in the upper hybrid resonance locations than the MW field as shown in **Figure 7(b)**. This evidence confirms that the electrostatic heating is being taking place at the UHR region where the magnetic field and plasma density satisfy the above-mentioned conditions [28]. To visualize the plasma density pattern due to these electric field behaviors, the radial distribution of the density is shown in **Figure 7(c)** for different time instances (i.e., 2, 5 and 85 μs) and axial planes on the cylindrical cavity during the plasma evolution. The plane z = 28 mm on the cavity is situated near the MW launching port. **Figure 7(c)** shows the plasma density to be more at the central location (z = 0 mm) than the location z = 28 mm that is located

ture is not yet stabilized during that time.

*DOI: http://dx.doi.org/10.5772/intechopen.92011*

toward the MW launch side.

**55**

#### **Figure 7.**

*(a) Temporal evolution of electron density and temperature during plasma formation time at point (r = 0, z = 28 mm) with gas pressure, 2 <sup>10</sup><sup>3</sup> mbar. (b) Temporal variation of MW electric field and plasma generated ambipolar electric field, the two main constituents of total electric field. (c) Radial profile of plasma density at three different time instants (t = 2 μs, 5 μs and 85 μs), at two axial locations during evolution of the plasma.*

#### *Evolution of Microwave Electric Field on Power Coupling to Plasma during Ignition Phase DOI: http://dx.doi.org/10.5772/intechopen.92011*

Correspondingly, the plasma density also reaches above the critical density. The decrease in the plasma bulk temperature and the corresponding increase of the plasma density even above the critical density are attributed to be occurring from the off-ECR or ES surface wave heating mechanisms [29, 30]. In other words, although the plasma density is approaching steady state (**Figure 7a**), the temperature is not yet stabilized during that time.

To confirm the off-resonance or electrostatic heating methods as discussed above, the evolution of the MW electric field and the electrostatic electric field is shown simultaneously in **Figure 7(b)**. The radial distribution of the two types of the electric field is given in that figure for two discrete time instants and the corresponding plasma densities. One can observe that the MW electric field is significant throughout the cavity and is more than the electrostatic electric field for the time, t = 500 ns. For another instance, t = 2 μs, the electrostatic electric field becomes more than the MW electric field throughout the cavity. The electrostatic field is even more in the upper hybrid resonance locations than the MW field as shown in **Figure 7(b)**. This evidence confirms that the electrostatic heating is being taking place at the UHR region where the magnetic field and plasma density satisfy the above-mentioned conditions [28]. To visualize the plasma density pattern due to these electric field behaviors, the radial distribution of the density is shown in **Figure 7(c)** for different time instances (i.e., 2, 5 and 85 μs) and axial planes on the cylindrical cavity during the plasma evolution. The plane z = 28 mm on the cavity is situated near the MW launching port. **Figure 7(c)** shows the plasma density to be more at the central location (z = 0 mm) than the location z = 28 mm that is located toward the MW launch side.

From the above-mentioned results (**Figures 6** and **7**), it can be commented that the power is absorbed by the ECR mechanism especially in the plasma condition where the density is below (underdense plasma) the critical density and slightly above the critical density (overdense plasma). If one notices the plasma parameters for the underdense conditions, one can observe that the density remains below the critical density from the time, t = t = 45 ns to t = 110 ns*.* In this case, the plasma electrons are magnetized and hence are following the magnetic field lines. The field free zones that are located near (r, z) = (0, 0) are being filled by the plasma particles because of the diffusion processes. Due to the ECR heating, the electron temperature is being increased in the field free zones in the underdense plasma situation, t < 110 ns. As the magnetic field lines are stronger (B 2300–2600 G) near the radial locations of the cavity, i.e., in the gaps of the two pairs of ring magnets, the plasma bulk electron temperature exhibits a sharp gradient in those regions. The maximum plasma bulk electron temperature achievable is 85 eV that occurs during the time, t = 280 ns*.* The high energy part of the plasma bulk electrons is being concentrated completely in the same gap as mentioned before during this time.

It is observed that the plasma bulk electron temperature increases in the radial direction at the regions mainly in between the two pairs of the ring magnets with the increase in time from t = 280 ns to 730 ns [22]. Therefore, it can be summarized that with the increase in plasma density (or time, t = 45 ns to t = 280 ns) from underdense to overdense state, the plasma bulk temperature is increased by an amount of 80 eV mainly in the radial direction near the region, 24 mm < r < 40 mm, 25 mm < z < 25 mm. This is because the ECR surfaces lie in those regions. The continuous heating through ECR in this location causes the high energy part of the plasma electron temperature to be concentrated on the same location even in the overdense plasma state during the time t = 730 ns.

The anisotropic behavior of the plasma bulk electron temperature even in the overdense plasma signifies the ECR heating [31, 32]. With further increase of time after the MW launch, i.e., near t = 2000 ns, the plasma bulk temperature (Te) is

**Figure 7.**

*Selected Topics in Plasma Physics*

**54**

*(a) Temporal evolution of electron density and temperature during plasma formation time at point (r = 0, z = 28 mm) with gas pressure, 2 <sup>10</sup><sup>3</sup> mbar. (b) Temporal variation of MW electric field and plasma generated ambipolar electric field, the two main constituents of total electric field. (c) Radial profile of plasma density at three different time instants (t = 2 μs, 5 μs and 85 μs), at two axial locations during evolution of the plasma.*

decreased to �10–12 eV. This range lies close to the thermal electron temperature. Therefore, the reduction of the high energy component of the plasma bulk temperature can be argued as the minimal occurrence of ECR heating process and correspondingly the initiation of the electrostatic heating mechanisms in the same time frame [29–31, 33]. The plasma reaches steady state after 2000 ns (2 μs) (**Figure 7a**). At the saturation, the plasma density is approximately 2 times more (�1.3 � 10<sup>17</sup> m�<sup>3</sup> ) than the critical density. During the same instant of time, the plasma electron temperature and its gradient reduce in the location where the magnetic field is relatively lower.

In order to investigate the different coupling mechanisms involved during the plasma evolution process and their impacts on the plasma parameters, the behavioral pattern of the different components of the electric field (Er and Ez) is shown in **Figures 8–10**. The power coupling mechanisms are ECR, UHR and polarity reversal related to ES heating. The particular type of coupling mechanism is understood from the electric field evolution pattern throughout the cavity. The electric field characters can be useful to characterize the plasma parameters based on the theoretical and experimental proofs. The proofs say the higher the plasma density, the more the power absorbed by the plasma.
