LongitudinalDynamics#

Longitudinal beam dynamics

Functions

`BunchLength()`	bunch length due to the potential well effect
`RFacc()`	Computes the RF acceptance with linear formula
`atBunchLength()`	bunch length due to the potential well effect
`atRFacc()`	Computes RF acceptance of the ring
`atSetCavityPhase()`	SETCAVITYPHASE Set the TimeLag attribute of RF cavities
`atsetcavity()`	ATSECAVITY Set the parameters of RF cavities
`cavityon()`	turns Cavities ON
`mcf()`	momentum compaction factor
`nus()`	Computes synchrotron tune from RF parameters
`phis()`	phase = (U0MeV,VrfMV)

BunchLength()#: bunch length due to the potential well effect

the output is the zerocurrent bunch length x bunch lengthening

bl = BunchLength (Ib,Zn,Vrf,U0,E0,h,alpha,sigdelta,circ)

Ib is the bunch current [A] (it may be a vector for multiple values)

Zn is the longitudinal broadband impedance [Ohms]

Vrf is the RF voltage [V] (it may be a vector for multiple values)

U0 is the energy loss around the ring [eV]

E0 is the beam energy [eV]

h is the harmonic number

alpha is the momentum compaction factor

sigmadelta is the energy spread

circ is the ring circumference

see also: atBunchLength

RFacc(vrf, u0, e0, h, alpha)#: Computes the RF acceptance with linear formula

delta_max_rf = RFacc(vrf,u0,e0,h,alpha)

This function computes the RF acceptance

Vrf is the RF voltage in V

U0 is the energy loss per turn in eV

E0 is the energy of the beam in eV

h is the harmonic number

alpha is the momentum compaction factor

See also atRFacc()

atBunchLength(ring, ib, zn)#: bunch length due to the potential well effect

the output is the zerocurrent bunch length x bunch lengthening

bl = atBunchLength(ring,ib,zn)

Ib is the bunch current [A] (it may be a vector for multiple values)

Zn is the longitudinal broadband impedance [Ohms]

ring is the at ring without radiation

BL is the bunch length in metres

see also: BunchLength

atRFacc(ring)#: Computes RF acceptance of the ring

delta_max_rf = atRFacc(ring)

The functions computes the RF acceptance of the ring

ring is tha at lattice without radiation

delta_max_rf is the RF acceptance

See also RFacc()

atSetCavityPhase()#: SETCAVITYPHASE Set the TimeLag attribute of RF cavities

NEWRING=SETCAVITYPHASE(RING)

Adjust the TimeLag attribute of RF cavities based on frequency,

voltage and energy loss per turn, so that the synchronous phase is zero.

An error occurs if all cavities do not have the same frequency.

NEWRING=SETCAVITYPHASE(…,’refpts’,CAVPTS)

CAVPTS is the location of RF cavities. This allows to ignore harmonic

cavities.

WARNING: This function modifies the time reference,

this should be avoided

NEWRING=SETCAVITYPHASE(…,’method’,METHOD)

Choose the method for computing the energy loss per turn

METHOD: ‘integral’: (default) The losses are obtained from

Losses = Cgamma / 2pi * EGeV^4 * I2

Takes into account bending magnets and wigglers.

‘tracking’: The losses are obtained by tracking without cavities.

Needs radiation ON, takes into account all radiating elements.

atsetcavity(ring, ..., 'frequency', frequency, ...)#: ATSECAVITY Set the parameters of RF cavities

atsetcavity may be used in two modes:

Upgrade mode

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By default, atsetcavity will act on the “main” cavities: they are defined by the

cavpts ring property, or if absent by cavities at the lowest frequency.

newring=atsetcavity(ring,…,’frequency’,frequency,…)

Set the cavity frequency [Hz]. FREQUENCY is a scalar or an array as

long as the list of selected cavities

newring=atsetcavity(ring,…,’frequency’,’nominal’,…)

Set the cavity frequency to the nominal value according to

circumference and harmonic number

newring=atsetcavity(ring,…,’frequency’,’nominal’,’dp’,dp)

Set the cavity frequency to the nominal value for the specified dp

newring=atsetcavity(ring,…,’frequency’,’nominal’,’dct’,dct)

Set the cavity frequency to the nominal value for the specified dct

newring=atsetcavity(ring,…,’frequency’,’nominal’,’df’,df)

Set the cavity frequency to the nominal value + df

newring=atsetcavity(ring,…,’voltage’,voltage,…)

Set the total voltage (all cells) [V]. VOLTAGE will be distributed over the

cells: CELL_VOLTAGE = VOLTAGE / PERIODICITY.

Then if CELL_VOLTAGE is a scalar, it will be equally shared among the

selected cavities. Otherwise it is an array as long as the list of

selected cavities.

newring=atsetcavity(ring,…,’harmnumber’,h,…)

Set the harmonic number. H is a scalar or an array as

long as the list of selected cavities

newring=atsetcavity(ring,…,’timelag’,timelag,…)

Set the time lag [m], . TIMELAG is a scalar or an array as

long as the list of selected cavities

newring=atsetcavity(ring,…,’cavpts’,cavpts)

CAVPTS is the location of the selected RF cavities. The default is to act on the

“main” cavities: they are defined by the cavpts ring property, or if absent by

cavities at the lowest frequency.

NOTES

1. In this mode, the radiation state of the lattice is not modified.

Compatibility mode

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newring = atsetcavity(ring,rfv,radflag,harm_number)

RING Ring structure

RFV RF voltage (full ring) [V]

RADFLAG 0/1: activate/desactivate radiation (atradon/atradoff)

HARMNUMBER Harmonic number (full ring)

NOTES

1. This mode is deprecated and should be replaced by

ring=atsetcavity(ring,’frequency’,’nominal’,’harmnumber’,harm_number, ‘voltage’,rfv)

RING=atSetCavityPhase(RING) (optional)

RING=atenable_6d(RING) (optional)

2. All the N cavities will have a voltage RFV/N

3. sets the synchronous phase of the cavity assuming radiation is turned

on radflag says whether or not we want radiation on, which affects

synchronous phase.

See also atSetCavityPhase(), atsetRFCavity(), atenable_6d(), atdisable_6d(), atgetU0()

cavityon(energy)#: turns Cavities ON

cavityon looks for elements that have field Frequency

and sets PassMethod for them to RFCavityPass

cavityon(energy)

In addition sets the E0 field of the global variable GLOBVAL

to energy - design energy [eV]

If GLOBVAL does not exist cavityon creates it

See also cavityoff(), radiationon(), radiationoff(), setcavity()

mcf(ring)#: momentum compaction factor

mcf(ring) calculates momentum compaction factor of RING

mcf(ring,dpp) computes the momentum compaction for off-momentum DPP

IMPORTANT!!!

mcf gives a wrong result with 6-d rings. The RING should be set to 4d.

See also atdisable_6d(), check_6d()

nus()#: Computes synchrotron tune from RF parameters

nus = nus (VrfMV, alpha, U0MeV, E0MeV, h)

this function return the synchrotron tune

input:

VrfMV is the RF voltage in MV

alpha is the momentum compaction factor

U0MeV is the energy lost per turn in MeV

E0MeV is the beam energy in MeV

h is the harmonic number

phis()#: phase = (U0MeV,VrfMV)

this function returns the synchronous phase in radians

input:

U0MeV is energy loss per turn in MeV

VrfMV is the RF voltage in MV