I guess, that if you set the field, you would not allow for the reflected wave at source plane, therefore you probably have no rise in amplitude?

I agree: while one end of the cavity (z=L, being L the length of the cavity) is actually behaving as a PEC, the other one (z=0) is not, because you are imposing the field there. Since you impose the field distribution at z=0, you will not see any reflection at z=0, simply because you are not actually calculating them.

You are not constantly feeding energy into the system by exciting with the continuous sine, but rather enforcing a boundary condition at your source plane. Thus, after an initial transient period you are getting the steady state harmonic field distribution conforming with your given geometrical and excitation boundary conditions.

I agree. I think the physical process is similar to 1d string continuously oscillated at one side and fixed at the other. You do not allow the reflection at the end of the cavity to accrue and hence it does not behave as a Fabry-Perot cavity or a 1d resonator.

I agree too. You are not put power into the system but only enforcing the E field distribution at section z=0 and at section z=L (there, the TM field is zero because it is a PEC wall). So, you find the steady state solution. In particular, you should use the equivalent transmission line equations. Look at the book "Time Harmonic electromagnetic fields" (Harrington ) in the chapter on cylindrical wave. There you find formulas about cylindrical cavities.

First of all thank you all for your answers.

Thinking about it more clear, it's the same problem as force a string to oscillate with one end free and the other fixed. But what about reflections? In Allen Taflove's book hard sources retroreflect the wave.This source I guess it's a hard source, so it should reflect back the wave incident on it. Where am I wrong?

no, it is like a string oscillating with both fixed ends. In fact, in your problem, you fix the field at z=0 to an assigned value and at z=L you put a PEC, so forcing the field to

zero

Dimitris

I don't have the book at hand. Could you reproduce your equation at z=0 in 1d sense as no need for all the components here? We perhaps could tell more.

Er(n+1,k)=Er(n)+A*{Hz(f)-Hz(f-1)}/df + B{Hf(k)-Hf(k-1)}/dz

Where Er(n) is calculated for k=0 (z=0) from the drive function as

Er(k=0)=Csin(ωt)

Where n refers to time step, A,B constants , df,dz angle and distance increments and C constant given by the space distribution of a specific mode

Same for the Ef component

I assume you have another equation for H with the source?

It seems that you are not adding the source field but equating to it.

Just as an experiment move the source in and add it to the field enforcing pec at boundaries.

I think that your problem can be solved in the frequency domain. That is write E(z,t)=real(Ef*exp(iωt)) where Ef is the complex fasor representing the field. In your case Ef(z=0)=Cexp(i*pi/2) ) and Ef(z=L)=0.

Then, Ef(z)=Ef(0)cos(bz)-i*Hf(0)*Z*sin(bz) holds, where: b is the wavenumber, depending on ω, geometry of the cylinder (radius) and materiel filling the cylinder; Z is the impedence, also depending on geometry and material. Hf(0) can be calculated by 0=Ef(0)cos(bL)-iH(0)*Z*sin(bL)

No I have not another equation for H field. I've observed that even with E field as source, H field can be "created". Moving in and out the source doesn't change the situation a lot. It creates a discontinuity at source position (because we set the field explicitly) and this equals to 1D problem of 2 string with fixed ends and movable start.

Unfortunately I don't want to solve the problem in frequency domain. The purpose of my code is to solve em propagation in time domain. Mode excitation is for checking the code rather than taking some results

My advise is to look up Jackson's solutions in "Electrodynamics" book. I remember him having an analytic solution for this geometry. If not him then Balanis' "Electromagnetics" book should definitely have it.

Dimitris

Are you solving only curl H Maxwell equation and not using the curl E one at all?

Maybe I miss something. When you solve your problem in terms of E-field, the H-field is implicitly included, in the sense that it exists (otherwise Maxwell would turn in his grave!). So, you solve the wave equation in E (second order derivatives in time and space) and then, if you want to find H, you can use the curl of E. But the point is that you are not feeding power in your system. You are only fixing a boundary condition! So you find a steady state solution. In order to convince yourself calculate the Poynting vector flux (avera

ged in time) at the section where you fix the E-field. You should find zero.

Dmitry and Andriana, I solve the full set of descritized Maxwell equations (3 for E field and 3 for H field). But I impose only E field distribution as the source. I let the code find the H field through update (H field needs E field and so on)

ok, so, if I understand well, you solve the first order derivative equations in time domain. It is ok. But it does not change the point: you do NOT have a source, you fix a boundary condition (at any time t, I guess). Moreover, your field is a time harmonic one at a fixed frequency. So, it is correct that, after a time transient, your solution does NOT explode. In fact you are not putting new power into the system. Or, to say better, the power goes in and out in a time period passing from the section at which you fixed the E-field (of course, nothing passes form the PEC section). Make the proof: calculate the Poynting vector (amplitude and direction) at the section z=0.

I assume any kind of drive function - eg Gaussin pulse, Sinc pulse etc, imposed with this way, will lead to the same results (not "explosion" in results).So, how the power is being imported into structure? I assume by the adding the source term. Moreover, this kind of source is called "Hard source" in the literature. But, from the conversation above, I understood that it's not a source rather than a boundary condition.

Dear Dimitris, sorry the delay in giving some answer, I am busy with teaching,

and always have some important paperwork to do.

You are imposing two boundary conditions at both ends of the waveguide, one side you impose the excitation and at the other side e_tangential=0. Physically means that at one side you have incident + reflected field = your stimulus (Gaussian, etc... in the time domain) at the other side you have a metal boundary. FDTD works with these two boundary conditions, and the field oscilates in the waveguide-resonator following these boundary conditions and Maxwell curls' equations. The field never blows up. The numerical field always is bounded, that corresponds to the real world of a waveguide with a fixed input and a short circuit at the other end. Similar to a standing wave pattern (for a given frequency). If the numerical field blows up that means you are calculationg something wrong, usually a calculation overlapping.

I hope I helped you. You can dowload my papers about FDTD from here, they are very didactic. If you want my papers that are not listed here let me know and I will send you privately. I do work in FDTD since 1989 (long ago). I served in the Editorial Board of IEEE, MTT, AP, etc....

I you find

Regards,

Enrique A. Navarro

Universitat de Valencia

Maxwell eqns are multi-D hyperbolic systems. Its linear convective part may let people think it's easier to handle compared to quasi-linear fluid mechanics eqns, but it's only partly true. In particular, the inclusion of sources in the eqns, especially low-regularity ones (spikes, oscillating or discontinuous) may lead to several numerical issues.

My first, and probably naive question would be: did you check that this absence of concentration in the middle of the cavity is stable to mesh refinement ? More generally, is your numerical soln very sensitive to the mesh ?

Hi Dimitris,

Because you impose the field to be equal to the excitation at the boundary corresponding to the source plane, you create an absorption of the reflected wave at this boundary (like Mur's absorbing condition). It is logical that the field between the source and the PEC boundary will be only composed of the incident field and the field reflected one time by the PEC boundary, creating a standing wave behaviour. I suggest to add a PEC boundary before the source plane. Also, the field in the source plane should include the FDTD update equations with the excitation as a current source.

I don't know if this can help you for your problem.

I need the code ,can you send it to me?my email is :[email protected]