numerics - Trying to solve a transcendental equation involving Bessel functions

I've never used Mathematica before and am trying to numerically solve equation (12) from this paper. Ideally I'd be able to find the smallest value of $x_{n\nu}$ for $\exp(-kr\pi)$ close to 1, and close to 0 for some range of $\nu$ (must be larger than 2) and then plot it.

I've tried a few methods I found after googling, but none seem to work.

I tried to use this by writing:

f= (2*BesselJ[a, x] + 
      x*(BesselJ[a + 1, x] + BesselJ[a - 1, x]))*(2*
       BesselY[a, x*exp[-Pi]] + 
      x*exp[-Pi]*(BesselY[a + 1, x*exp[-Pi]] + 
         BesselY[a - 1, x*exp[-Pi]])) - (2*BesselY[a, x] + 
      x*(BesselY[a + 1, x] + BesselY[a - 1, x]))*(2*
       BesselJ[a, x*exp[-Pi]] + 

      x*exp[-Pi]*(BesselY[a + 1, x*exp[-Pi]] + 
         BesselY[a - 1, x*exp[-Pi]]));
 sol[_a] = NSolve[f ==0 && x>0 && x < 10 && a > 2 && a < 12, x, Reals);

and was told that NSolve can't solve it.

I've also tried using

sol[a_] := x /. FindRoot[f, {{x, 0}, {a, 2}}]; 

which throws up an error:

SetDelayed::write : Tag Plus in *My definition of f here*[a_, x_] is Protected.