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rodarima / cpic

Particle in Cell simulation of plasma in C
GNU General Public License v3.0
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Wrong harmonic frequency #23

Open rodarima opened 4 years ago

rodarima commented 4 years ago

The simple electron pair bounce at a different frequency than expected. The theoretical period is of 14.2 seconds, but the experimental is 10.4 seconds.

iter=   1 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000000e+00 1.600000e+01)  r1=(2.800000e+01 1.600000e+01)
iter= 207 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000363e+00 1.600000e+01)  r1=(2.799964e+01 1.600000e+01)
iter= 208 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000656e+00 1.600000e+01)  r1=(2.799934e+01 1.600000e+01)
iter= 414 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000043e+00 1.600000e+01)  r1=(2.799996e+01 1.600000e+01)
iter= 620 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000156e+00 1.600000e+01)  r1=(2.799984e+01 1.600000e+01)
iter= 826 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000978e+00 1.600000e+01)  r1=(2.799902e+01 1.600000e+01)
iter= 827 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000180e+00 1.600000e+01)  r1=(2.799982e+01 1.600000e+01)
iter=1033 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000033e+00 1.600000e+01)  r1=(2.799997e+01 1.600000e+01)
iter=1239 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000611e+00 1.600000e+01)  r1=(2.799939e+01 1.600000e+01)
iter=1240 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000399e+00 1.600000e+01)  r1=(2.799960e+01 1.600000e+01)
iter=1446 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000001e+00 1.600000e+01)  r1=(2.800000e+01 1.600000e+01)
iter=1652 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000328e+00 1.600000e+01)  r1=(2.799967e+01 1.600000e+01)
iter=1653 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000702e+00 1.600000e+01)  r1=(2.799930e+01 1.600000e+01)
iter=1859 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000057e+00 1.600000e+01)  r1=(2.799994e+01 1.600000e+01)
iter=2065 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000134e+00 1.600000e+01)  r1=(2.799987e+01 1.600000e+01)
iter=2271 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000922e+00 1.600000e+01)  r1=(2.799908e+01 1.600000e+01)
iter=2272 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000204e+00 1.600000e+01)  r1=(2.799980e+01 1.600000e+01)
iter=2478 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000023e+00 1.600000e+01)  r1=(2.799998e+01 1.600000e+01)
iter=2684 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000568e+00 1.599996e+01)  r1=(2.799943e+01 1.600004e+01)
iter=2685 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(4.000436e+00 1.599996e+01)  r1=(2.799956e+01 1.600004e+01)
iter=2891 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(3.999934e+00 1.599419e+01)  r1=(2.800007e+01 1.600581e+01)
iter=3095 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(3.988828e+00 1.512723e+01)  r1=(2.801117e+01 1.687277e+01)
iter=3096 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(3.978425e+00 1.510344e+01)  r1=(2.802157e+01 1.689656e+01)
iter=3097 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(3.971761e+00 1.507877e+01)  r1=(2.802824e+01 1.692123e+01)
iter=3098 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(3.968834e+00 1.505317e+01)  r1=(2.803117e+01 1.694683e+01)
iter=3099 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(3.969634e+00 1.502664e+01)  r1=(2.803037e+01 1.697336e+01)
iter=3100 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(3.974149e+00 1.499913e+01)  r1=(2.802585e+01 1.700087e+01)
iter=3101 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(3.982358e+00 1.497064e+01)  r1=(2.801764e+01 1.702936e+01)
iter=3102 wp=4.419417e-01 T=1.421723e+01 ni=284.3  r0=(3.994234e+00 1.494114e+01)  r1=(2.800577e+01 1.705886e+01)
rodarima commented 4 years ago

Given the current experiments, in a system with two equal charges enclosed in a 2D periodic space of size L, the electric field at one of the charges is not proportional to a cosine. Therefore, the plasma frequency equation doesn't necessarily hold for this experiment. The theoretical values for the field match closely (with relative error < 2%) the electric field computed with the simulation. Then the solver seems to be working fine. err3 In any case, we still need either a simulation where the frequency can be computed, or derive the frequency from the theoretical electric field.