Dispersion relation in cylindrical plasma column

[ghasem007]

Hi.
is there anyone who is familiar with surface wave plasma discharges?
I want to solve dispersion equation of surface waves in cylindrical plasma column,numerically,to obtain "phase diagram" and "attenuation diagram" from dispersion equation solving.
But this dispersion equation include in bessel functions with complex argument (my unknown in this equation is within bessel argument).
But,in MATLAB this problem can not solve,efficient.
is there anyone who help me?

5 my equation is as following:

I want find all of zeros below equation.
εr*t0*besseli(1,tp*a)*besselk(0,t0*a)+tp*besse lk(1 ,t0*a)*besseli(0,tp*a)=0
where:
tp=√(k^2-εr*k0^2)
t0=√(k^2-k0^2)
k0=ω/c.
c is light velocity,a,ω,εr,k0 are real constant and known.
t0 and tp are in terms of k.k is complex,i.e it has real & imagianry parts.

besseli and besselk are modified bessel functions of first and second type.

in above equation all of quantities are known except k,that k is zero of equation.

i want to find zeros of above,i.e i want find values of k.

by using of "fsolve command" i guess my roots are not perfectly true.
i don't now how find all of zeros in equation exactly.
please help me...

 

[LightHero]

It sounds like you need to use a numerical root-finding algorithm to solve your equation. MATLAB has several built-in functions for solving nonlinear equations numerically, such as fsolve and fzero. You could also use an open-source numerical solver such as SciPy or Apache Commons Math.