Lattice Properties

General parameter

Basic format of the general parameters are,

keyword1 = "value1";
keyword2 = "value2";
...

keyword	value	description
sim_type	“MomentMatrix”	Simulation mode. FRIB simulation uses the particular mode “MomentMatrix”.
MpoleLevel	“0”, “1”, or “2”	Multipole term controller for the rf cavities. “0” - only include focusing and defocusing effect “1” - include dipole terms “2” - include dipole and quadrupole terms
EmitGrowth	“0” or “1”	Flag for cross-cavity emittance growth effect. “0” - False (no emittance growth) “1” - True (calculate emittance growth)
HdipoleFitMode	“0” or “1”	Flag for auto-adjustment of bending element “0” - use “bg” or “beta” for the bending strength “1” - auto-adjust the bending strength

Beam parameter

Basic format of the beam parameters are,

keyword1 = value1;
keyword2 = [value2, value3]; # list input
...

keyword	value	description
IonEs	float	Nucleaon mass of the reference beam. [eV/u]
IonEk	float	Initial kinetic energy of the reference beam. [eV/u]
SampleFreq	float	Sampling frequency. [Hz] (default is 80.5e6 [Hz])
IonChargeStates	list of float	List of charge to mass ratios of the all charge states. [1] The first element is used as the reference beam.
NCharge	list of float	List of macro weights of the all charge states. [1]
${vector_variable}${n}	vector[7]	Initial centroid vector of the n-th charge state. ${vector_variable} is defined in `source`. $[x, x', y, y', \phi, E_k, 1]$ with [mm, rad, mm, rad, rad, MeV/u, 1]
${matrix_variable}${n}	vector[49]	Flattened initial envelope matrix of the n-th charge state. ${matrix_variable} is defined in `source`. Cartisan product of $[x, x', y, y', \phi, E_k, 1]^2$ with [mm, rad, mm, rad, rad, MeV/u, 1] $^2$
Eng_Data_Dir	string	Directory path of the rf cavity data. `dir(path)` supports relative path.

Lattice elements

Basic format of the one lattice element is,

name_of_element1: element_type, parameter1 = value1, parameter2 = value2, ... ;

After writing down the all lattice elements, user need to specify the lattice cell and the cell to USE.

# define the cell
name_of_cell: LINE = ( name_of_element1, name_of_element2, name_of_element3, ... );

# set the cell to USE
USE: name_of_cell;

element_type	description
`source`	Starting point of the simulation.
`marker`	Marker element.
`stripper`	Chage stripper element.
`tmatrix`	User input transfer matrix.
`orbtrim`	Orbit trim element.
`drift`	Drift space element.
`solenoid`	Solenoid magnet element.
`quadrupole`	Magnetic quadrupole element.
`sextupole`	Magnetic sextupole element.
`equad`	Electrostatic quadrupole element.
`sbend`	Magnetic bend element.
`edipole`	Electrostatic dipole element.
`rfcavity`	RF cavity element.

Special element

type source

Starting point of the simulation. Initial beam state parameters are set at this element.

Parameters

vector_variable: string

Name key of the initial centroid vector.

matrix_variable: string

Name key of the initial envelope matrix.

type marker: Marker element. Nothing to do.

type stripper

Stripper element.

Parameters

IonChargeStates: list of float

List of charge to mass ratios after the charge stripper. [1]

charge_model: string

Macro weight model for stripper.

- “baron” (default): Use Baron formula for the macro weights.

- “off”: Use NCharge parameter for the macro weights.

NCharge: list of float

List of macro weights after the charge stripper. [1]

This list length must be same as the IonChargeStates

This parameter is used only in the case of charge_model = "baron".

Stripper_IonZ: float (optional, default is 78.0/238.0)

Charge to mass ratio of the reference beam. [1]

Stripper_IonMass: float (optional, default is 238.0)

Ion mass of the reference beam. [amu]

Stripper_IonProton: float (optional, default is 92.0)

Proton number of the reference beam. [1]

Stripper_E1Para: float (optional, default is 2.8874e-3)

Constant part of the energy struggling parameter of the charge stripper. [MeV/u]

Stripper_lambda: float (optional, default is 5.5740)

Momentum spread factor $\lambda$ of the charge stripper. [1]

Stripper_upara: float (optional, default is 2.6903)

Momentum spread factor $U$ of the charge stripper. [1]

The momentum spread is defined as $\sqrt(U/\lambda^2)$ [mrad].

Stripper_E0Para: vector[3] (optional, default is [16.348e6, 1.00547, -0.10681])

Energy loss parameters due to the ionization.

[Constant_part, Energy_dependence, Thickness_depenedence] with [eV/u, 1, 1]

Stripper_Para: vector[3] (optional, default is [3.0, 20.0, 16.623e6])

Stripper foil parameters.

[Thickness, Thickness_variation, reference_energy] with [um, %, eV/u]

type tmatrix

User input transfer matrix element.

Parameter: matrix: vector[49]

Flattened $7 \times 7$ transfer matrix.

Optical element

type orbtrim

Orbit trim element. This can be use as steering magnet.

Parameters

realpara: int

Realistic input parameter flag for the beam kick angle.

0 - use theta_x and theta_y for the beam kick.

1 - use tm_xkick and tm_ykick for the beam kick.

theta_x: float

Horizontal beam kick angle. [rad]

theta_y: float

Vertical beam kick angle. [rad]

tm_xkick: float

Magnetic field strength for the horizontal beam kick. [T*m]

tm_ykick: float

Magnetic field strength for the vertical beam kick. [T*m]

xyrotate: float

Transverse rotation angle of the beam. [deg]

Note

In the case of user puts both “beam kick information” and “transverse rotation angle” to the ONE orbtrim element, the process order is, transverse rotation -> beam kick. In other words, the beam kick is effected AFTER the transverse rotation.

type drift

Drift space element.

Parameters: L: float

Length of the lattice element. [m]

type solenoid

Solenoid magnet element.

Parameters

L: float

Length of the lattice element. [m]

B: float

Solenoid strength ($B_z$). [T]

dx: float (default: 0.0)

Misalignment of horizontal shift. [m]

dy: float (default: 0.0)

Misalignment of vertical shift. [m]

pitch: float (default: 0.0)

Misaglignment of pitch angle. [rad]

yaw: float (default: 0.0)

Misaglignment of yaw angle. [rad]

roll: float (default: 0.0)

Misaglignment of roll angle. [rad]

ncurve: int (default: 0)

Number of curves for slanted and overlapped field.

(0 means hard-edge fringe model)

scl_fac${n}: float (default: 0)

Scaling factor of the n-th curve (n start from 0).

Unit of scl_fac${n}*curve${n} is [T].

curve${n}: vector

n-th Curve information (n start from 0).

Each curve vector must have the same size. The vector elements should be defined by the scaled strength of the element at the step. Also, the step size is defined by “L divided by the size of curve${n}”.

CurveFile: string

External file name for the curves, the file format is the same as curve${n}.

e.g. curve0 = [1.0, 2.0, …];

If CurveFile is available, it overrides the curve${n}.

use_range: vector[2]

Use range of curve${n}. Format is [start_id, end_id].

type quadrupole

Magnetic quadrupole element.

Parameters

L: float

Length of the lattice element. [m]

B2: float

Quadrupole field gradient. [T/m]

Positive value means horizontal focusing.

dx, dy, pitch, yaw, roll: float

Misalignment parameters. See solenoid case.

ncurve, scl_fac${n}, curve${n}, CurveFile, use_range

Curve inputs for slanted and overlapped field. See solenoid case.

Unit of scl_fac${n}*curve${n} is [T/m].

type sextupole

Magnetic sextupole element.

Parameters

L: float

Length of the lattice element. [m]

B3: float

Sextupole field gradient. [T/m^2]

Positive value means horizontal focusing.

dstkick: bool

On/off flag to calculate the centroid shift due to the 3rd order effect.

Default is 1 (on).

step: int

Step number for the sextupole element. Default is 1.

dx, dy, pitch, yaw, roll: float

Misalignment parameters. See solenoid case.

type equad

Electrostatic quadrupole element.

Parameters

L: float

Length of the lattice element. [m]

V: float

Electrostatic quadrupole pole tip voltage. [V]

Positive value means horizontal focusing.

radius: float

Electrostatic quadrupole pole tip radius. [m]

dx, dy, pitch, yaw, roll: float

Misalignment parameters. See solenoid case.

ncurve, scl_fac${n}, curve${n}, CurveFile, use_range

Curve inputs for slanted and overlapped field. See solenoid case.

Unit of scl_fac${n}*curve${n} is [V/m^2].

type sbend

Magnetic bend (dipole) element.

Parameters

L: float

Length of the lattice element. [m]

phi: float

Bend angle. [deg]

phi1: float

Front pole face angle. [deg]

phi2: float

Back pole face angle. [deg]

bg: float (optional: Used in the case of “HdipoleFitMode” is 0.)

Lorentz $\beta \gamma$ for the reference beam. [1]

This parameter is correspond to the bend field strength.

dx, dy, pitch, yaw, roll: float

Misalignment parameters. See solenoid case.

type edipole

Electrostatic dipole (bend) element.

Parameters

L: float

Length of the lattice element. [m]

phi: float

Bend angle. [deg]

beta: float (optional: Used in the case of “HdipoleFitMode” is 0.)

Lorentz $\beta$ for the reference beam. [1]

This parameter is correspond to the bend field strength.

fringe_x: float

Horizontal fringe term. [rad/mm]

fringe_y: float

Vertical fringe term. [rad/mm]

asymfac: float

Characteristic parameter of the kinetic energy change due to the middle point potential deviation from ground. [1]

spher: int

Flag for the electrostatic dipole shape.

0 - cylindrical electrostatic dipole

1 - spherical electrostatic dipole

ver: int

Flag for the bending direction.

0 - horizontal bend

1 - vertical bend

dx, dy, pitch, yaw, roll: float

Misalignment parameters. See solenoid case.

type rfcavity

RF cavity element.

Parameters

L: float

Length of the lattice element. [m]

cavtype: string

Cavity type. Supports “Generic”, “0.041QWR”, “0.085QWR”, “0.29HWR”, and “0.53HWR”. The file format is described here.

f: float

RF frequency of the cavity. [Hz]

phi: float

Input phase of the cavity. [deg]

syncflag: int

Flag for synchronous phase input (for above parameter phi).

0 for driven phase input.

1 for synchronous phase input with complex fit model. (default)

2 for synchronous phase input with sinusoidal fit model.

scl_fac: float

Scaling factor of the field. [1]

datafile: string (optional: Used in the case of cavtype = “Generic”)

File path of the rf cavity data.

Rm: float (optional: Used in the case of cavtype = “Generic”)

Characteristic radial length of the multipole expansion. [mm]

dx, dy, pitch, yaw, roll: float

Misalignment parameters. See solenoid case.

Rf cavity data format

FLAME using Thin-Lens-Model for rf cavity calculation. Rf cavity data is composed of “Longitudinal axis data”, “Multipole lattice data”, “Multipole field data”, and “TTF fitting data”.

Hard-coded FRIB cavity models

For typical rf cavity in FRIB, the “TTF fitting data” is hard-coded in FLAME. Following files are required for each rf cavity type.

cavtype	Longitudinal axis data	Multipole lattice data	Multipole field data
“0.041QWR”	“axisData_41.txt”	“Multipole41/thinlenlon_41.txt”	“Multipole41/CaviMlp_41.txt”
“0.085QWR”	“axisData_85.txt”	“Multipole85/thinlenlon_85.txt”	“Multipole85/CaviMlp_85.txt”
“0.29HWR”	“axisData_29.txt”	“Multipole29/thinlenlon_29.txt”	“Multipole29/CaviMlp_29.txt”
“0.53HWR”	“axisData_53.txt”	“Multipole53/thinlenlon_53.txt”	“Multipole53/CaviMlp_53.txt”

Generic rf cavity model

FLAME supports lattice format input for the generic rf cavity model.

The basic format of the rf cavity data is similar to the main lattice file,

Rm = value1;

Ez = [
z1, Ez1,
z2, Ez2,
z3, Ez3,
...
];

name_of_element1: element_type, parameter1 = value1, parameter2 = value2, ... ;
...

cell: LINE =(name_of_element1, ...);
USE: cell;

keyword	value	description
Rm	float	Characteristic radial length of the multipole expansion. [mm]
Ez	vector[2*n]	On axis $E_z$ data. The odd index (1,3,5,…) is z position. [mm] The even index (2,4,6,…) is Electric field strength. [V/m]
RefNorm	float	Reference normalization factor for complex synchronous phase definition. This value is defined by $q A/m$ where $A$ is the scaling factor of the 3D EM field. If RefNorm or SyncFit are not defined, sinusoidal model is used for the synchronous phase definition.
SyncFit	vector[5*n]	Fitting parameters for complex synchronous phase definition. The fitting model is shown here.
EnergyLimit	vector[2]	Lower and higher limit for incident energy. [MeV] This value is used for warning signs only.
NormLimit	vector[2]	Lower and higher limit for normalization factor. This value is used for warning signs only.

Lattice element for the rf cavity data

Drift space is the same format as the main lattice but unit of L is [mm] - drift

type EDipole

Dipole term generated by the electric field.

Parameters

L: float

Length of the lattice element. [mm]

This parameter should be 0.0 in Thin-Lens-Model.

V0: float

Amplitude of the multipole term. [MV]

attr: vector[20]

TTF fitting parameter. (see here)

1 to 10 - fitting parameter for $T$

11 to 20 - fitting parameter for $S$

type EFocus

Constant focusing term generated by the electric field.

Parameters are the same as EDipole.

type EQuad

Quadrupole term generated by the electric field.

Parameters are the same as EDipole.

type HMono

Dipole term generated by the magnetic field.

Parameters

L: float

Length of the lattice element. [mm]

This parameter should be 0.0 in Thin-Lens-Model.

V0: float

Amplitude of the multipole term. [MA]

attr: vector[20]

TTF fitting parameter. (see here)

1 to 10 - fitting parameter for $T$

11 to 20 - fitting parameter for $S$

type HFocus

Constant focusing term generated by the magnetic field.

Parameters are the same as HMono.

type HQuad

Quadrupole term generated by the magnetic field.

Parameters are the same as HMono.

type AccGap

Acceleration gap term by the longitudinal electric field.

Parameters

L: float

Length of the lattice element. [mm]

This parameter should be 0.0 in Thin-Lens-Model.

V0: float

Amplitude of the multipole term. [MV]

attr: vector[23]

TTF fitting parameter. (see here)

1 to 10 - fitting parameter for $T$

11 to 20 - fitting parameter for $S$

21 to 23 - fitting parameter for the synchronous phase

Note

FLAME is using TTF-calculation acceleration technique to boost cavity modeling speed. TTF factor $T$ and $S$ are pre-calculated and fitted using 9th order polynomial function according to different particle phase speed $k$. $n$-th fitting parameter $p_n$ is listed as,

\[T(k), S(k) = \sum^9_{n=0} p_n k^{(9-n)}.\]

The driven-phase calculation is also boosted by using fitting model for the energy gain curve.

For the sinusoidal fitting model, the phase transferring factor $\varphi_c$ is fitted by using

\[\varphi_c = p_0 E^{p_1} + p_2.\]

Here, $E$ is the kinetic energy and $p_{i = 0, 1, 2}$ are the fitting parameters.

For other complex models (e.g. peak-base model), the phase transferring factor depends on the normalization factor $g = q A/m$ where $A$ is the scaling factor of the 3D EM field. The fitting model for $\varphi_c$ is,

\[\varphi_c = \sum_{i=0}^n (p_{5i} E^{p_{5i+1}} + p_{5i+2} \ln(E) + p_{5i+3}e^E + p_{5i+4})\times g^i .\]

Here, user can determine $n$ value corresponds to the size of SyncFit.

The driven phase $\varphi_d$ is calculated by using $\varphi_c$,

\[\varphi_d = \varphi_s - \varphi_c - m \varphi_\text{abs}\]

where, $\varphi_s$ is the synchronous phase in input, $\varphi_\text{abs}$ is absolute phase in front of the rf cavity, and $m$ is the harmonic number.