at.physics.nonlinear#

Non-linear optics

Functions

`detuning`(ring[, xm, ym, npoints, nturns])	Computes the tunes for a sequence of amplitudes
`chromaticity`(ring[, method, dpm, npoints, ...])	Computes the non-linear chromaticities
`gen_detuning_elem`(ring[, orbit])	Generates a detuning element
`tunes_vs_amp`(ring[, amp, dim, nturns])	Generates a range of tunes for varying x, y, or z amplitudes

chromaticity(ring, method='linopt', dpm=0.02, npoints=11, order=3, dp=0, **kwargs)[source]#

Computes the non-linear chromaticities

This function computes the tunes for the specified momentum offsets. Then it fits this data and returns the chromaticity up to the given order (npoints>order)

Parameters:

ring (Lattice) – Lattice description
method (str | None) –
'linopt' (dfault) returns the tunes from the linopt6() function,

'fft' tracks a single particle and computes the tunes with fft,

'laskar' tracks a single particle and computes the tunes with NAFF.
dpm (float | None) – Maximum momentum deviation
npoints (int | None) – Number of momentum deviations
order (int | None) – Order of the fit
dp (float | None) – Central momentum deviation

Returns:

fit (ndarray) – Horizontal Vertical polynomial coefficients from numpy.polyfit of shape (2, order+1)
dpa – dp array of shape (npoints,)
qz – tune array of shape (npoints, 2)

detuning(ring, xm=3e-05, ym=3e-05, npoints=3, nturns=512, **kwargs)[source]#

Computes the tunes for a sequence of amplitudes

This function uses tunes_vs_amp() to compute the tunes for the specified amplitudes. Then it fits this data and returns the detuning coefficiant dQx/dx, dQy/dx, dQx/dy, dQy/dy and the qx, qy arrays versus x, y arrays

Parameters:

ring (Lattice) – Lattice description
xm (float | None) – Maximum x amplitude
ym (float | None) – Maximum y amplitude
npoints (int | None) – Number of points in each plane
nturns (int | None) – Number of turns for tracking
method – 'laskar' or 'fft'. Default: 'laskar'
num_harmonics – Number of harmonic components to compute (before mask applied)
fmin – Lower bound for tune
fmax – Upper bound for tune
hann – Turn on Hanning window. Default: False

Returns:

q0 (ndarray) – qx, qy from horizontal and vertical amplitude scans. Fit results with shape (2, 2)
q1 (ndarray) – Amplitude detuning coefficients with shape (2, 2) [[dQx/dx, dQy/dx], [dQx/dy, dQy/dy]]
x (ndarray) – x amplitudes (npoints, )
q_dx (ndarray) – qx, qy tunes as a function of x amplitude (npoints, 2)
y (ndarray) – y amplitudes (npoints, )
q_dy (ndarray) – qx, qy tunes as a function of y amplitude (npoints, 2)

gen_detuning_elem(ring, orbit=None)[source]#

Generates a detuning element

Parameters:

ring (Lattice) – Lattice description
orbit (ndarray | None) – Avoids looking for initial the closed orbit if it is already known ((6,) array).

Returns:

detuneElem – Element reproducing the detuning of the ring with amplitude and momentum

tunes_vs_amp(ring, amp=None, dim=0, nturns=512, **kwargs)[source]#

Generates a range of tunes for varying x, y, or z amplitudes

Parameters:

ring (Lattice) – Lattice description
amp (Sequence[float] | None) – Oscillation amplitude. If amp is None the tunes are calculated from linopt6() else tracking is used
dim (int | None) – Coordinate index of the oscillation
nturns (int | None) – Number of turns
method – 'laskar' or 'fft'. Default: 'laskar'
num_harmonics – Number of harmonic components to compute (before mask applied)
fmin – Lower bound for tune
fmax – Upper bound for tune
hann – Turn on Hanning window. Default: False

Returns:

tunes (ndarray) – Array of tunes qx, qy with shape (len(amp), 2)