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lines changed Original file line number Diff line number Diff line change @@ -31,19 +31,19 @@ namespace picongpu
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* no transverse spacial envelope
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* based on the electric potential
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* Phi = Phi_0 * exp(0.5 * (x-x_0)^2 / sigma^2) * cos(k*(x - x_0) - phi)
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- * by applying grad Phi = d/dx Phi = E(x)
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+ * by applying - grad Phi = - d/dx Phi = E(x)
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* we get:
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- * E = Phi_0 * exp(0.5 * (x-x_0)^2 / sigma^2) * [k*sin(k*(x - x_0) - phi) + x/sigma^2 * cos(k*(x - x_0) - phi)]
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+ * E = - Phi_0 * exp(0.5 * (x-x_0)^2 / sigma^2) * [k*sin(k*(x - x_0) - phi) + x/sigma^2 * cos(k*(x - x_0) - phi)]
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*
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* This approach ensures that int_{-infinity}^{+infinity} E(x) = 0 for any phase
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* if we have no transverse profile as we have with this plane wave train
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*
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* Since PIConGPU requires a temporally defined electric field, we use:
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* t = x/c and (x-x_0)/sigma = (t-t_0)/tau and k*(x-x_0) = omega*(t-t_0) with omega/k = c and tau * c = sigma
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* and get:
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- * E = Phi_0*omega/c * exp(0.5 * (t-t_0)^2 / tau^2) * [sin(omega*(t - t_0) - phi) + t/(omega*tau^2) * cos(omega*(t - t_0) - phi)]
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+ * E = - Phi_0*omega/c * exp(0.5 * (t-t_0)^2 / tau^2) * [sin(omega*(t - t_0) - phi) + t/(omega*tau^2) * cos(omega*(t - t_0) - phi)]
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* and define:
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- * E_0 = Phi_0*omega/c
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+ * E_0 = - Phi_0*omega/c
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* integrationCorrectionFactor = t/(omega*tau^2)
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*
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* Please consider:
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