# Dispersion relation in cylindrical plasma column

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1. May 11, 2013

### 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.