Beta dependence in transverse resistive wall wake

[DavidPost-1]

Lines 614-619 of wakes.py define the transverse resistive wall wake:

def wake(dt, *args, **kwargs):
    y = (Yokoya_factor * (np.sign(dt + np.abs(self.dt_min)) - 1) / 2. *
            np.sqrt(kwargs['beta']) * self.resistive_wall_length / np.pi /
            self.pipe_radius**3 * np.sqrt(-mu_r / np.pi /
            self.conductivity / dt.clip(max=-abs(self.dt_min))))*np.sqrt(Z_0*c)
    return y

As I understand it, for a Yokoya factor of 1 this equivalent to

$$ W_{1, \perp}^{\textrm{PyHT}}(z) = \frac{\textrm{sgn}(z)-1}{2} \sqrt{\beta} \frac{L}{\pi b^3} \sqrt{\frac{\beta c}{\pi \sigma |z|}} \sqrt{Z_0 c} = \frac{\textrm{sgn}(z)-1}{2} \frac{L}{b^3} \sqrt{\frac{\mu_0 \beta^2 c^3}{\pi^3 \sigma}} \frac{1}{\sqrt{|z|}}. $$

The expected form of this wake can be found in Equation 130 of F. Zimmerman's paper, "Resistive-wall wake and impedance for nonultrarelativistic beams" with the $|z|^{-5/2}$ term neglected, which for reference is

$$ W_{1, \perp}(z) = \frac{\textrm{sgn}(z)-1}{2} \frac{L}{b^3} \sqrt{ \frac{\mu_0 \beta^3 c^3}{\pi^3 \sigma} } \frac{1}{\sqrt{|z|}}. $$

Compared to this, $W_{1, \perp}^{\textrm{PyHT}}(z)$ seems to be missing a factor of $\sqrt{\beta}$. Is this expected?

Many Thanks.