Description of the element "rfq" for a Radio-Frequency Quadrupole Linac *********************************************************************** Element entry in the lattice file "sclinac.dat": ------------------------------------------------ ncells rfq vol len rad phase harm nstep nfile ncells: Number of RFQ cells vol: Vane Voltage in kV len: RFQ Length in cm rad: RFQ Radius in cm phase: RFQ Input phase: input to main RFQ, after the input matcher harm: Harmonic number according to the base frequency nstep: Number of integration steps per cell nfile: RFQ file # for cells data file (RFQ.#nf) Example: -------- 269 rfq 90.45 310.0 0.34 0.0 1.0 100 11 Data in the RFQ cells data file: RFQ.#nf (RFQ.#01 for nf=1): ------------------------------------------------------------ For a regular cell the columns in the RFQ file RFQ.#nf are: Cell Length Voltage Radius Modulation Type A01 A10 A03 A12 A21 A23 A30 A32 # (cm) (kV) (cm) (none) (none) - - - - - - - - --------------------------------------------------------------------------------------- Cell: Cell number Length: Cell length (cm) Radius: Cell radius (cm) Voltage: Vane voltage (kV) Modulation: Cell modulation Type: Cell type A01: Quadrupole focusing term A10: Accelerating term A03: Higher order focusing term A12: Higher order accelerating term A21: Higher order term A23: Higher order term A30: Higher order term A32: Higher order term Cell Types: ---------- Type = 0: Regular cell -1: Input matcher section, may include few cells (not necessary an integer number) -2: Input transition cell: Crandall type -3: Step-wise input matcher, every line is a step with different radius -4: Input transition cell: Half-Cell type 1: Output matcher section, may include few cells (not necessary an integer number) 2: Output transition cell: Crandall type 3: Step-wise output matcher, every line is a step with different radius 4: Output transition cell: Half-Cell type Description of the 8-term potential coefficients in the RFQ input file RFQ.#nf: ------------------------------------------------------------------------------- For a regular cell, the general form of the 8-term potential is given by : U(r,th,z) = V/2 * { C1 * r^2 * cos(2*th) + C2 * r^6 * cos(6*th) + C3 * I0(k*r) * cos(k*z) + C4 * I4(k*r) * cos(4*th) * cos(k*z) + C5 * I2(2*k*r) * cos(2*th) * cos(2*k*z) + C6 * I6(2*k*r) * cos(6*th) * cos(2*k*z) + C7 * I0(3*k*r) * cos(3*k*z) + C8 * I4(3*k*r) * cos(4*th) * cos(3*k*z) } where (r,th,z): are the cylindrical coordinates with th=theta, the azimuthal angle V: is the vane voltage C1-8: are the 8 coefficients of the 8-term potential. I0-6: are the Bessel functions from 0 to 6th order k: pi/L, where L=beta*lambda/2 is the cell length To be able to directly compare the relative strengths of the 8 terms, we use the normalized coefficients instead of the "C" coefficients defined above, except for the accelerating term C3 (A10). The actual 8-term potential expression used in TRACK is: U(r,th,z) = V/2 * { A01 * (r/R)^2 * cos(2*th) + A03 * (r/R)^6 * cos(6*th) + A10 * I0(k*r) * cos(k*z) + A12 * I4(k*r)/I4(k*R) * cos(4*th) * cos(k*z) + A21 * I2(2*k*r)/I2(2*k*R) * cos(2*th) * cos(2*k*z) + A23 * I6(2*k*r)/I6(2*k*R) * cos(6*th) * cos(2*k*z) + A30 * I0(3*k*r)/I0(2*k*R) * cos(3*k*z) + A32 * I4(3*k*r)/I4(2*k*R) * cos(4*th) * cos(3*k*z) } where R: is the cell average radius The normalized coefficients used for TRACK input as function of the "C" coefficients above are: A01 = C1 * R^2 A03 = C2 * R^6 A10 = C3 A12 = C4 * I4(k*R) A21 = C5 * I2(2*k*R) A23 = C6 * I6(2*k*R) A30 = C7 * I0(2*k*R) A32 = C8 * I4(2*k*R) Description of the input data for non regular cells: ---------------------------------------------------- Input/Output Matcher: Cell Type: -1/1 -------------------- Cell Length Voltage Radius Modulation Type A01 A03 LR0 Dfl # (cm) (kV) (cm) (none) (none) - - (cm) (cm) ------------------------------------------------------------------- where LR0: Length of the straight section with Radius R0 at the inner end of matcher. Dfl: Fall parameter of the curved section, it is typically 13/12*(Length-LR0). Input/Output Transition: Cell Type: -2/2, Crandall type ----------------------- Cell Length Voltage Radius Modulation Type A01 A10 # (cm) (kV) (cm) (none) (none) - - --------------------------------------------------------- Input/Output Matcher: Cell Type: -3/3, Step-wise type -------------------- Cell Length Voltage Radius Modulation Type A01 # (cm) (kV) (cm) (none) (none) - ---------------------------------------------------- Input/Output Transition: Cell Type: -4/4, Half-Cell type ----------------------- Cell Length Voltage Radius Modulation Type A01 A10 LRG # (cm) (kV) (cm) (none) (none) - - (cm) -------------------------------------------------------------- where LRG: Length of the regular part = Half length of a regular cell at the same beta If (Length-LRG) is non zero, there will be a straight section of radius R0 before (type:-4) or after (type:4) the regular half cell. More description of the different cell types can be found in TRACKv37 Manual.