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I want to simulate a resonator cavity with a medium inside with FDTD method. The medium has a resonant frequency $\omega_R$. I want to find ratio of outgoing $P_{out}$ power to the incoming power $P_{in}$ at the frequency $\omega$:

$A(\omega)= \frac{P_{out}}{P_{in}}$

Currently, I use a continuous wave (CW) source at a fixed frequency. I slowly ramp the amplitude of the source and wait until the the steady state. I added a small damping to the medium. But even with the damping the resonance causes numerical problems, since the amplitude becomes very large at the resonance.

The question:

Is possible to use a pulsed source and still be able to obtain $A(w)$? This way the amplitude, will not become too large and numerical problems will be avoided. I am worried that the steady state is not achieved when the pulse is used as a source.

Appendix:

The simulations are in 2D. The medium is a magnetized plasma. The geometry is shown in the figure below. A cavity filled with a plasma. The incoming power $P_in$ and outgoing power  $P_out$

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    $\begingroup$ "media" is the plural of "medium" $\endgroup$ – flippiefanus Jun 18 '18 at 10:49
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It sounds to me like you are interested in the resonator quality factor $Q$ (please correct me if I'm wrong), which can be roughly defined as $$ Q = \frac{\mbox{stored energy}}{\mbox{energy dissipated per period}}. $$

Since you are using a pulsed source, I guess you want to use the ring-down method to estimate $Q$: switching-off the driving signal leads to a decay of the stored energy (due to the dissipation) and the decay time $\tau$, the $1/e$ time, is proportional to $Q$, $$ Q = \tau\cdot\omega_R, $$ with the resonance frequency of the system $\omega_R$.

To finally answer your question, yes, in my understanding it should definitely be possible to measure the quality factor with a pulsed source in your FDTD-code.

The numerical instability you mentioned is a separate topic, does that occur at the metallic walls? If so, how have you modelling/realized your metal walls?

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