Conversion to boosted-frame

class fbpic.lpa_utils.boosted_frame.BoostConverter(gamma0)

Initialize the object by calculating the velocity of the boosted frame.

Parameters:

gamma0 (float) – Lorentz factor of the boosted frame

boost_particle_arrays(x, y, z, ux, uy, uz, inv_gamma)

Transforms particles to the boosted frame and propagates them to a fixed time t_boost = 0. without taking any electromagnetic effects into account. (This is useful for the initialization of a bunch distribution in the boosted frame.)

Parameters:

• x (1darray of float (in meter)) – The position of the particles in the lab frame (One element per macroparticle)

• y (1darray of float (in meter)) – The position of the particles in the lab frame (One element per macroparticle)

• z (1darray of float (in meter)) – The position of the particles in the lab frame (One element per macroparticle)

• ux (1darray of floats (dimensionless)) – The momenta of the particles (One element per macroparticle)

• uy (1darray of floats (dimensionless)) – The momenta of the particles (One element per macroparticle)

• uz (1darray of floats (dimensionless)) – The momenta of the particles (One element per macroparticle)

• inv_gamma (1darray of floats (dimensionless)) – The inverse of the Lorentz factor (One element per macroparticle)

Return type:

The same arrays (in the same order) but in the boosted frame

copropag_density(lab_frame_vars, beta_object=1.0)

Converts a list of densities that correspond to copropagating objects (e.g. an electron bunch) from the lab frame to the boosted frame, i.e: n’ = n * [ gamma0*(1 - beta_object*beta0) ]

Parameters:

• lab_frame_vars (list of floats) – A list containing several densities to be converted

• beta_object (float, optional) – The normalized velocity of the object whose density is being converted

Return type:

A list with the same number of elements, with the converted quantities

copropag_length(lab_frame_vars, beta_object=1.0)

Converts a list of lengths that correspond to copropagating objects (e.g. the laser) from the lab frame to the boosted frame, i.e: L’ = L / [ gamma0*(1 - beta_object*beta0) ]

Parameters:

• lab_frame_vars (list of floats) – A list containing several length to be converted

• beta_object (float, optional) – The normalized velocity of the object whose length is being converted

Return type:

A list with the same number of elements, with the converted quantities

gamma(lab_frame_vars)

Converts a list of Lorentz factors from the lab frame to the boosted frame: gamma’ = gamma0 * ( gamma - beta0 * sqrt( gamma**2 - 1 ) )

Warning: The above formula assumes that the corresponding particle has no transverse motion at all.

Parameters:

lab_frame_vars (list of floats) – A list containing several Lorentz factors to be converted

Return type:

A list with the same number of elements, with the converted quantities

interaction_time(L_interact, l_window, v_window)

Calculates the interaction time in the boosted frame: (Time it takes for the moving window to slide once across the total interaction length, i.e. the plasma)

L_interact’ = L_interact / gamma0 l_window’ = l_window * gamma0 * ( 1 + beta0 ) v_window’ = ( v_window - c * beta0 )/( 1 - beta0*v_window/c ) v_plasma’ = -beta0 * c

T_interact’ = L_interact’ + l_window’ / ( v_window’ - v_plasma’ )

Parameters:

• L_interact (float (in meter)) – The total interaction length (typically the length of the plasma) in the lab frame.

• l_window (float (in meter)) – The length of the moving window in the lab frame.

• v_window (float (in meter/second)) – The velocity of the moving window in the lab frame.

Returns:

T_interact – The interaction time in the boosted frame.

Return type:

float (in seconds)

longitudinal_momentum(lab_frame_vars)

Converts a list of momenta from the lab frame to the boosted frame: u_z’ = gamma0 * ( u_z - sqrt(1 + u_z**2) * beta0 )

Warning: The above formula assumes that the corresponding particle has no transverse motion at all.

Parameters:

lab_frame_vars (list of floats) – A list containing several momenta to be converted

Return type:

A list with the same number of elements, with the converted quantities

static_density(lab_frame_vars)

Converts a list of densities that correspond to static objects (e.g. the plasma) from the lab frame to the boosted frame, i.e: n’ = n * gamma0

Parameters:

lab_frame_vars (list of floats) – A list containing several length to be converted

Return type:

A list with the same number of elements, with the converted quantities

static_length(lab_frame_vars)

Converts a list of lengths that correspond to static objects (e.g. the plasma) from the lab frame to the boosted frame, i.e: L’ = L / gamma0

Parameters:

lab_frame_vars (list of floats) – A list containing several length to be converted

Return type:

A list with same number of elements, with the converted quantities

velocity(lab_frame_vars)

Converts a list of velocities from the lab frame to the boosted frame: v’ = ( v - c * beta0 )/( 1 - beta0*v/c )

Parameters:

lab_frame_vars (list of floats) – A list containing several velocities to be converted

Return type:

A list with the same number of elements, with the converted quantities

wavenumber(lab_frame_vars)

Converts a list of wavenumbers from the lab frame to the boosted frame: k’ = k / ( gamma0 ( 1 + beta0 ) )

Parameters:

lab_frame_vars (list of floats) – A list containing several wavenumbers to be converted

Return type:

A list with the same number of elements, with the converted quantities