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In this section, the EQUIPOT code is used to investigate the degree to which the equilibrium potential of a surface (which is exposed to a severe charging environment) depends on each of the characteristic surface and bulk properties of the material. A set of surface properties and plasma parameters were chosen such that EQUIPOT predicts a potential of -10.0 kV to develop on the "patch" material. This set of parameters provides a convenient datum against which the effect of changes in surface characteristics may be assessed. The "baseline" configuration consists of a sunlit aluminium sphere with a shadowed Kapton patch of thickness 51|im. The environment is a "double Maxwellian" which is close to the published "SCATHA worst-case substorm environment"104, but with a slight increase in the density of the higher temperature electron component in order to produce a patch potential of -9.98 kV (sufficiently close to the desired -10.0 kV) . The default list of material properties for aluminium and for Kapton are listed in Table 7.1, and the modified worst-case substorm environment is given in Table 7.2. This environment was chosen, rather than using results from Chapter 5 for two reasons; Firstly, the SCATHA worst case environment is commonly used as an input to NASCAP simulations and it is interesting to investigate how material parameters affect current balance equation solutions in this environment; Secondly it is supposed to be a worst-case environment, so that the results of a sensitivity analysis will be exaggerated, but clearly visible. Section 7.2 is devoted to investigating the effect of different plasma characteristics on the current balance equation solution; the severity of this environment relative to those derived from Meteosat data is therefore quantified.

Since the fraction of the aluminium covered by the Kapton patch is assumed to be negligible, the conduction current between the aluminium and Kapton may be ignored when computing the equilibrium potential of the aluminium (structure) material. This value is largely determined by the photoelectron temperature and turns out to be +6.7V relative to space plasma potential. All results presented for the remainder of this section assume that the structure is maintained at this constant potential. 7.1.1 Sensitivity to conduction

Although the conductivity current is usually a small fraction of the incident current, it can play a significant role in the current balance equation, especially close to equilibrium, where other components change very slowly with surface potential. EQUIPOT considers only the bulk

conductivity between the patch and the structure, and can incorporate field enhanced conductivity according to the model of Adamec and Calderwood68. Thus, there are four parameters which affect the conduction current; patch thickness, conductivity of the patch material, together with temperature and relative permittivity of the patch material, if

field enhanced conductivity is included.

Figure 7.1 shows the equilibrium potential of the Kapton patch as a function of Kapton thickness, for five different cases; (i) Assuming that the bulk conductivity current can be calculated according to Ohm's law (marked "Default"), (ii) Assuming field enhanced conductivity according to equation 3.110 with a patch temperature of 273K (marked "273K"), (iii) as for (ii), but with a patch temperature of 173K (marked "173K"), (iv) as for (ii) but with a patch temperature of 373K (marked “373K") and (v) as for (ii), but assuming that the relative permittivity of Kapton is 4.0. The three temperatures were chosen on the basis that these are the minimum, most probable, and maximum temperatures likely to be attained by satellite surface materials. At thicknesses of 1mm or greater, all five curves converge since the conductivity current becomes negligible for thick samples; the equilibrium potential is a result of detailed balancing of surface currents only. The most striking feature of these results, however, is the effect of including field enhanced conductivity, which appears to inhibit differential charging for thin dielectric films. Patch temperature has a significant effect on the enhancement of conductivity due to electric fields; as the temperature increases, the degree of enhancement is reduced, although this should be offset against the normal effects of temperature on bulk conductivity at low electric fields. The relative permittivity of Kapton is reported66 as lying between 3.0 and 4.0. According to Figure 7.1, a small change in relative permittivity has only a second order effect on the equilibrium potential of the Kapton patch compared to other factors.

There are several reported values for the bulk conductivity of Kapton; the differences perhaps arise from uncertainties in the various measurement techniques, slight differences in the characteristics of the sample, temperature effects or ageing. Figure 7.2 gives the effects of varying the bulk conductivity over almost four orders of magnitude, for Ohmic conduction only (marked "Normal" on the figure) and for field enhanced conductivity at 273K (marked "enhanced" on the figure). Two effects are apparent; the field enhancement effect is most important for low values of conductivity, and the equilibrium potential is especially sensitive to the conductivity when its value exceeds 10'15 mho/m.

7.1.2 Sensitivity to changes in electron backscatter

To estimate the current of backscattered electrons from a surface, EQUIPOT uses the model described in section 3.2.2, for which the only free parameter is the atomic number of the target material, Z. The sensitivity of the equilibrium potential to changes in Z for the target material were investigated by using the default configuration and

environment described earlier and varying the atomic number of the patch material (Kapton) . Variation of Z may be thought of as a convenient device for changing the importance of the backscattered electron current relative to the other components.

The results of this analysis are given in Figure 7.3. Z has been varied over atomic numbers from 5 to 90 which ensures that all possible backscatter yield functions are sampled. Although there is a significant variation in equilibrium potential over the full range of Z, the solution is relatively insensitive to small changes in Z. Also, the effect of making a small change in Z decreases slightly for high Z materials.

7.1.3 Sensitivity to changes In electron SEE current

The model for secondary emission of electrons due to electron impact described in section 4.1.2 is based on three parameters; the maximum yield at normal incidence, the energy of maximum yield, and the energy loss power. A sensitivity analysis over the full range of all three variables would generate a prohibitive number of results; however, if the study is confined to polymers, Burke's relations (equations 3.85, 3.86 and 3.87) can be used to relate both the maximum yield and energy at maximum yield to an “emission coefficient", K which is computed from the properties of a repeating polymeric unit. Thus, for polymers, a sensitivity analysis can be performed with two free parameters; K which can range from 0.682 (Kapton) through to 1.546 (Teflon) and the energy loss power, n which can range from about 1.3 to 2.3.

The results are shown in Figure 7.4 where the equilibrium potential has been plotted against n for several values of K, giving a family of curves. At high energies, beyond the peak in the yield curve, the secondary emission yield is inversely related to n. When n exceeds 2.0,

(for this severe environment), the current of secondary electrons is virtually suppressed, thus at high values of n, there is almost no dependence on K, and the equilibrium potential asymptotically approaches a value determined by the balance between incident current, backscatter, ion-induced SEE and conductivity. For each value of K, there is a threshold value of n, above which negative charging occurs. The position of this threshold also depends on the spectrum of incident radiation and represents the point where the incident electron current is exactly equal in magnitude to the sum of the true SEE current, backscatter, incident ion and ion-induced SEE currents. Just above this threshold value of n, the equilibrium potential increases rapidly for small changes in n such that if n is raised above the threshold by 0.1, the equilibrium potential may change by several kilovolts. In addition, that part of the curve just above the threshold value of n is the region where changes in K have their greatest effect, ie the vertical separation of the family of curves is at a maximum.

In summary, for a given polymer, the energy loss power must be measured with great care, especially if it lies close to the threshold value. The precision with which the position of maximum yield (or K

value) must be measured depends on the appropriate value of n for a given material. Previous measurements of the secondary yield properties of materials have tended to concentrate on determining the maximum yield, and the energy at which this occurs; this work has demonstrated that it is more important to concentrate on measuring the yield at high incident energy, from which n can be determined with greatest accuracy.

7.1.4 Sensitivity to changes in ion-induced SEE

Secondary electrons liberated from a surface as a result of ion impact (SEI) are modelled according to the theory described in section 3.2.3, which permits the secondary yield function to be characterised in terms of two parameters; the yield for normally incident, 1 keV protons, and the incident proton energy at which the normal yield is a maximum. Variation of two parameters is ideally suited to a sensitivity analysis, and a search of lists of material data from NASCAP19,44 revealed that for common satellite surface materials, the yield at 1 keV varies between 0.2 and 0.5, whilst the energy for maximum yield occurs between 100 and 300 keV.

Figure 7.5 shows the results of the analysis for the default configuration of a shaded Kapton patch subjected to a severe substorm environment. The effects of changing the energy of maximum yield are small since this energy is an order of magnitude greater than the temperature of the hottest plasma component. The sensitivity to changes in E„ will be further reduced for less severe environments. Changing the yield for 1 keV protons has a much greater effect, but large changes are necessary to cause the equilibrium potential to be affected significantly.

Although this current component is always a significant constituent of the current balance equation, it is relatively insensitive to small changes in the two properties which define the yield function. In addition, the sensitivity to variations in these two parameters will diminish as the spectrum softens.