slactrac.PWFA.Ions2D¶

class slactrac.PWFA.Ions2D(species, N_e, sig_r, sig_xi, r0_big=None, n_samp=1000, order=5, rtol=None, atol=None)[source]¶

A class to facilitate calculating ion motion in PWFA ion columns due to cylindrical, infinitely-long gaussian beams.

New in version 1.6.

Parameters:

Parameters:	species : `periodictable.core.Element` The plasma gas species, e.g. `periodictable.H`. N_e : float The number of electrons. sig_r : float The standard deviation in $r$ . sig_xi : float The standard deviation in $\xi$ . r0_big : float The maximum particle coordinate in $r$ to include. n_samp : int The number of samples. order : int The order to calculate to rtol : float A tolerance to calculate to. See `scipy.integrate.odeint`. atol : float A tolerance to calculate to. See `scipy.integrate.odeint`.

species : periodictable.core.Element

The plasma gas species, e.g. periodictable.H.

N_e : float

The number of electrons.

sig_r : float

The standard deviation in $r$ .

sig_xi : float

The standard deviation in $\xi$ .

r0_big : float

The maximum particle coordinate in $r$ to include.

n_samp : int

The number of samples.

order : int

The order to calculate to

rtol : float

A tolerance to calculate to. See scipy.integrate.odeint.

atol : float

A tolerance to calculate to. See scipy.integrate.odeint.

Attributes

`A`	Ion mass in units of AMU.
`N_e`	Number of electrons in bunch.
`atol`
`dims`	Number of dimensions.
`k`	Driving force term: $r'' = -k \left( \frac{1-e^{-r^2/2{\sigma_r}^2}}{r} \right)$
`k_small`	Small-angle driving force term: $r'' = -k_{small} r$ .
`lambda_small`	The wavelength for small ( $r_0 < \sigma_r$ ) oscillations.
`m`	Ion mass.
`nb0`	On-axis beam density $n_{b,0}$ .
`q_label`
`rtol`
`sig_r`	Transverse R.M.S.
`sig_xi`	Longitudinal R.M.S.
`species`	The species of gas used (see `periodictable.core.Element`).

Methods

`h`(q)
`lambda_large`(r0)	The wavelength for large ( $r_0 < \sigma_r$ ) oscillations.
`omega_big`(q0)
`q`(x, q0)	Numerically solved trajectory function for initial conditons $q(0) = q_0$ and $q'(0) = 0$ .
`r_large`(x, r0)	Approximate trajectory function for large ( $r_0 > \sigma_r$ ) oscillations.
`r_small`(x, r0)	Approximate trajectory function for small ( $r_0 < \sigma_r$ ) oscillations.