Laplace transform electric fields

If the excitation electric field is an s-polanzed evanescent field instead of the above p-polarized example, then wH 11 [ = wHJI(z)] does not depend upon p. Therefore, an approximate C(z) can be calculated from the observed fluorescence (P) (obtained experimentally by varying 0) by ignoring the z dependence in the bracketed term in Eq. (7.45) and by inverse Laplace transforming Eq. (7.44) after the ,(0, /J) 2 term has been factored out.,37 39)... 

Electron Drift in a Constant Electric Field. As an example, let us consider the system discussed in the time-of-flight section. In this system, charge carriers are generated close to the injecting contact and drift to the collecting contact under the force of a constant electric field. As discussed above, the current response on a laser pulse has a constant value of Jph = AQIr for 0 < t < t, and drops instantly to zero at t=r. The input signal is a delta function and the output response is a step function. Linear-response theory shows that the system function H s) is the Laplace transform of the impulse response function h(t). In our example ... 

Closer examination reveals that (VII-4) is no longer valid in these circumstances, because the Laplace transform integral (III-l) does not exist. Equation (VII-7), therefore, is restricted to values of e below the critical value defined by the inequality (VII-8) if the electric field is increased beyond this point the plasma breaks down into charged fragments. 

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