Sedov blast formula:
R=a*(E/p)^1/(2+n)*t^2/(2+n);
I want to calculate the deposition energy E by fitting between R and t. What are the units of R, t and p when using this formula?
And the calculated E is J or mJ?
[E]=J, [R]=m, [p]=kg/m3, [t]=sec, [a]=dimensionless.
Important note: the above formula gives correct dimension for radius R (in meters) ONLY for n=3. For arbitrary n, you will have a "fractal" dimension, namely [R]=m5/(n+2) . Check it out. See also section 10 from the attached chapter.
In fact, to use your Sedov formula for any spatial dimension n, one needs to assume that parameter a in that general formula is not dimensionless. More precisely, a=L(n-3)/(n+2) where L is some characteristic length (that is [L]=m) which could be related to R. Hence, only in 3D (when n=3) the parameter a is truely dimensionless. In 2D (n=2) and in 1D (n=1) we have a=L-1/4 and a=L-2/3, respectively. Something like this. Though I don't have any references to corroborate this assumption. The situation could be more complicated.
In addition to E, R and t, there are two parameters in that formula. Namely, density p and dimensionless parameter a. Which values are you using for these two parameters? Clearly, the absolute value of the energy will depend on their value. What is the REAL incident energy? How do you know it?
For spherical case, a=a(gamma, E,ro) its definition is presented in book Zeldovich Raizer Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena.
For laser-matter interaction, you should consider absorbed part of laser energy. If laser radiation is focused onto planar target then energy is doubled i.e. 2E should be in your formula.
the real energy is measured by an energy meter. the physical model is that a laser pulse ablates the glass. the propagation of laser induced shock wave is investigated in my experiment and i think that this can be depicted as a massless point blast process. the p=1.2kg/m3, a is got by fitting the r and t using sedov's spherical theory. @Sergei Sergeenkov
@Chao Shen: what is the obtained experimental value of the energy E?
@Chao Shen: I also need info about the maximum value of the obtained in your experiments R(t). Something like R=10mm at t=1000ns?
As Alexey pointed out, the dimensionless parameter a is not easy to estimate. If I use your experimental value for the energy E_exp=17mJ, my calculations suggest that a_exp=0.6. But if I use your theoretical value E_th=50mJ, the same fit results in a_th=0.49. Both estimates for parameter a are pretty close. What is your value for a?
Approach of point explosion should be checked. It seems to me that, for so small energies and big time scale, point explosion approximation is not valid. Absorption coefficient of air plasma is ~ 0.5(E~20 mJ) or 0.85 (E~50 mJ). Approximation of point explosion with counter-pressure should be used in your case for t > 100 ns.
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