Difference between revisions of "@notsosureofit Hypothesis"
m (Force derivation for tapered cylindrical EM cavity.) |
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Starting with the expressions for the frequency of a cylindrical RF cavity: | Starting with the expressions for the frequency of a cylindrical RF cavity: | ||
| − | f = (c/(2* | + | f = (c/(2*pi))*((X/R)^2+((p*pi)/L)^2)^.5 |
For TM modes, X = X[sub m,n] = the n-th zero of the m-th Bessel function. | For TM modes, X = X[sub m,n] = the n-th zero of the m-th Bessel function. | ||
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Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency. | Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency. | ||
| − | delta(f) = (1/(2*f))*(c/(2* | + | delta(f) = (1/(2*f))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2)) |
and from there the expression for the acceleration g from: | and from there the expression for the acceleration g from: | ||
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g = (c^2/L)*(delta(f)/f) such that: | g = (c^2/L)*(delta(f)/f) such that: | ||
| − | g = (c^2/(2*L*f^2))*(c/(2* | + | g = (c^2/(2*L*f^2))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2)) |
Using the "weight" of the photon in the accelerated frame from: | Using the "weight" of the photon in the accelerated frame from: | ||
Revision as of 12:49, 27 May 2015
The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)
Starting with the expressions for the frequency of a cylindrical RF cavity:
f = (c/(2*pi))*((X/R)^2+((p*pi)/L)^2)^.5
For TM modes, X = X[sub m,n] = the n-th zero of the m-th Bessel function. [1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.
and for TE modes, X = X'[subm,n] = the n-th zero of the derivative of the m-th Bessel function. [0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.
Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.
delta(f) = (1/(2*f))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2))
and from there the expression for the acceleration g from:
g = (c^2/L)*(delta(f)/f) such that:
g = (c^2/(2*L*f^2))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2))
Using the "weight" of the photon in the accelerated frame from:
"W" = (h*f/c^2)*g => "W" = T = (h/L)*delta(f)
gives thrust per photon:
T = (h/(2*L*f))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2))
If the number of photons is (P/hf)*(Q/2*pi*f) then:
NT = P*Q*(1/(4*pi*L*f^3))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2))
