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In the previous sections, the axial ion transport behaviour showed that the major differences between the standard and extension cases could be explained by the change in the axial potential profile resulting from the different plasma density profiles. To understand why the density profile has been affected in this way, the electron transport throughout the chamber can be studied. To begin, the RF-compensated Langmuir probe was swept radially just above the beginning of the potential drop atz=−15 cm in 1 cm increments to assess any changes

in electron heating in the source region. Figure 4.8a shows the EEPFs measured by the RF-compensated probe using the second derivative method (equation 2.6) at z = −15 cm,

r = 0 cm for both cases. The EEPFs shown in figure 4.8a are plotted relative to their

the compensated probe demonstrated the same increase as shown earlier in figure 4.4 at

z = −15 cm. The EEPFs in the figure demonstrate very similar behaviour, however in

the extension case, there is a larger population of electrons in the distribution, which is in agreement with the slightly higher density at this location shown in figure 4.3.

0 10 20 30 40 50 60 (eV) -5 -4 -3 -2 -1 0 1 2 3 ln(EEPF) (a) -6 -4 -2 0 2 4 6 r-axis (cm) 0 2 4 6 8 10 12 14 16 18 T eff (eV) (b)

Figure 4.8: Measurements of the electron behaviour atz=−15cm. (a) The EEPFs measured

on axis for the standard (solid line) and extension (dashed line) using the second derivative method for finding the EEPF. (b) The calculated values of Tef f as a function of the radial

position.

Figure4.8bshows the radial profile of the effective electron temperature,Tef f, calculated

using equation 2.8. From the profiles, it can be determined that the radial electron temper- ature is not significantly affected by the addition of the extension tube even though there is a higher density plasma on axis. The values of electron temperature also match those presented previously in the Chi Kung reactor under similar experimental conditions [67].

At z= −15 cm, the magnetic field strength is around 130 Gauss, which means that the

electron Larmor radii, r_Le, for electron temperatures of 8 and 16 eV are 0.5 and 0.7 mm,

respectively. These values are of the order of the RF-compensated Langmuir probe tip radius, i.e. rLe∼rp. It is therefore unclear if the values ofTef f found here using the second derivative

method for measuring the EEPF are accurate given that this method is only strictly valid for unmagnetised plasmas, i.e. for r_p << r_Le. On the other hand, the first derivative method is

only strictly valid forr_Le<< r_p, showing that neither method is explicitly valid, however the

method. Figure4.9 shows the values ofT_{ef f} calculated using the first and second derivative

methods for the standard and extension cases. In each of the standard and extension cases, the calculated values of Tef f using the first derivative method are within the ±1 eV error

bars of the second derivative method. This comparison allows for use of the second derivative method throughout the chamber.

-6 -4 -2 0 2 4 6 r-axis (cm) 0 2 4 6 8 10 12 14 16 18 T eff (eV)

(a) Standard case.

-6 -4 -2 0 2 4 6 r-axis (cm) 0 2 4 6 8 10 12 14 16 18 Teff (eV) (b) Extension case.

Figure 4.9: The effective electron temperature calculated when using the first (squares) and second (triangles) derivative methods for calculating the EEPF in a magnetised plasma.

It is now important to determine if a change in the effective electron temperature would be expected with the addition of the extension tube. As a quick guide, a particle balance for a low pressure, unmagnetised, cylindrical plasma can be undertaken to see if a change in electron temperature should be expected with an increase in source tube length. The particle balance here follows the standard method presented in [3], equating the rates of ion loss to the walls and ion creation in plasma chamber, i.e.

A_lossc_s=n_gV K_iz (4.4)

whereA_lossis the effective loss area of the walls of the chamber,n_gis the neutral gas density,V

is the volume of the cylindrical plasma chamber andK_iz is the ionisation rate as a function of Tegiven byKiz = 2.34×10

−14

Te0.59e

−17.44/T e_{. The effective loss area is given by the physical}

area of the radial and end walls of the cylindrical volume, each scaled by the centre-to-edge ratio for low pressure cylindrical plasmas:

where L and R are the length and radius of the cylinder, respectively, and h_L andh_R are the

axial and radial centre-to-edge ratios, respectively, given by

h_L= 0.86 3 + L 2λ_i −1/2 (4.6) hR= 0.80 4 + R λi −1/2 (4.7) whereλ_i= _σ1

ing is the ion neutral mean free path and σi is the ion collision cross section.

Solving equations 4.4 - 4.7 for 0.3 mTorr, σ_i= 1×10−18 m2 and R=6.8 cm for cases

of L=31 cm and L=49.5 cm, corresponding to the lengths of the standard and extension cases, respectively, the electron temperature is found. The results of the particle balance give electron temperatures of 6.8 eV and 6.6 eV for the standard and extension cases, respectively, showing that the electron temperature is only expected to change by less than 3% with the addition of the extension tube. These calculated electron temperatures are displayed by horizontal lines on figure 4.8band, on axis, are not too dissimilar from the measured values.