TuneAndChromaticity#

Tune and chromaticity

Functions

`findtune()`	get the tune value from turn by turn positions
`fitchrom2()`	fits chromaticity of THERING using 2 sextupole families
`fittune2()`	fits linear tunes of THERING using 2 quadrupole families
`intfft()`	Calculates the tune from interpolated FFT of the trajectory.
`tunechrom()`	computes linear tunes and chromaticities

findtune(pos, method)#: get the tune value from turn by turn positions

tune=findtune(pos,method)

POS: Tune-by-turn particle position

METHOD: Method for tune determination:

1: Highest peak in fft

2: Interpolation on fft results

3: Windowing + interpolation

[tune,spectrum]=findtune(…) Also returns the fft

fitchrom2(newchrom, sextupolefamily1, sextupolefamily2)#: fits chromaticity of THERING using 2 sextupole families

fitchrom2(newchrom,sextupolefamily1,sextupolefamily2)

fittune2(newtunes, quadfamily1, quadfamily2)#: fits linear tunes of THERING using 2 quadrupole families

fittune2(newtunes,quadfamily1,quadfamily2)

[dk, jinv] = fittune2(newtunes,quadfamily1,quadfamily2)

intfft(x)#: Calculates the tune from interpolated FFT of the trajectory.

intfft(x) X must be a column vector.

If X is a matrix - each column is treated as

a separate trajectory

intfft(x,guess,delta) searches for peaks in the FFT spectrum

only within the range (X-DELTA … X+DELTA)

The same values of GUESS and DELTA are used for all columns of X

tunechrom(ring)#: computes linear tunes and chromaticities

tune=tunechrom(ring) Quick calculation of the fractional part of the tune

from numerically computed transfer matrix.

[tune, chrom] = tunechrom(ringd,dp,’get_chrom’) - optionally computes the

chromaticities by numerical differentiation from the difference between

tune values at momentums DP+0.5*DPStep and DP-0.5*DPStep

**[…]=tunechrom**(…,’orbit’,ORBITIN Do not search for closed orbit.

Instead ORBITIN,a 6x1 vector of initial conditions is used:

This syntax is useful to avoid recomputing the closed orbit if is

already known;

[…]=tunechrom(ring,dp) (obsolete)

[…]=tunechrom(ring,…,’dp’,dp) Specify the momentum deviation when

radiation is OFF (default: 0)

[…]=tunechrom(ring,…,’dct’,dct) Specify the path lengthening when

radiation is OFF (default: 0)

[…]=tunechrom(ring,…,’df’,df) Specify the RF frequency deviation when

radiation is OFF (default: 0)

Note: tunechrom computes tunes and chromaticities from the one-turn

transfer matrix. The transfer matrix is computed from tracking using

numerical differentiation. The error of numerical differentiation

is sensitive to the step size. (Reference: Numerical Recipes)

The calculation of tunes involves one numerical differentiation.

The calculation of chromaticity involves TWO!!! numerical differentiations.

The error in calculated chromaticity from may be substantial (~ 1e-5).

Use the XYStep and DPStep keyword arguments to control the step size

in chromaticity calculations

See also atlinopt6()