TY - ELEC
AU - Louis, R.
PY - 1971
TI - The properties of ion orbits in the central region of a cyclotron
KW - Report
LA - eng
M3 - Text
AB - The behaviour of ion orbits in the magnetic and electric fields at the
centre of a cyclotron is studied in detail. The objective is to optimize
the phase acceptance and beam quality for a 500 MeV H⁻ isochronous
cyclotron.
Since accurate electric fields are necessary for orbit calculations,
a numerical method for calculating those fields is examined in detail. The
method is suitable for complicated electrode shapes and converges rapidly,
yielding potentials in three dimensions with average errors of less than
0.01%. The magnetic fields used in the orbit calculations are measured on
model magnets.
The axial motions are examined using a thick lens approximation for
the accelerating gaps. A method is demonstrated for calculating the axial
acceptance of the cyclotron as a function of RF phase. This method is used
to evaluate the merits of various central geometries and injection energies.
This method is also used to examine the effects of flat-topping the RF
voltage by adding some third harmonic to the fundamental waveform. It is
found that addition of the optimum amount of third harmonic increases the
phase acceptance by about 20 deg. Finally, the effects of field bumps on
the axial motions are investigated.
To allow accurate radial motion calculations to high energy, an
approximate formula is developed which yields accurate (<1%) values for the
changes in orbit properties of an ion crossing a dee gap. The geometry of
the orbit on the first turn is discussed in detail. The radial centring is
studied by tracking ions from injection to 20 MeV, and a method is
described for choosing the starting conditions of the beam so as to minimize
the radial betatron amplitude over a desired phase range.
The problems associated with using a three-fold symmetric magnetic
field with a two-fold symmetric electric field are also discussed. Besides
the well-known gap-crossing resonance, a previously ignored phase-oscillation
effect is found to be important for cyclotrons operating on a
high harmonic of the ion rotation frequency.
N2 - The behaviour of ion orbits in the magnetic and electric fields at the
centre of a cyclotron is studied in detail. The objective is to optimize
the phase acceptance and beam quality for a 500 MeV H⁻ isochronous
cyclotron.
Since accurate electric fields are necessary for orbit calculations,
a numerical method for calculating those fields is examined in detail. The
method is suitable for complicated electrode shapes and converges rapidly,
yielding potentials in three dimensions with average errors of less than
0.01%. The magnetic fields used in the orbit calculations are measured on
model magnets.
The axial motions are examined using a thick lens approximation for
the accelerating gaps. A method is demonstrated for calculating the axial
acceptance of the cyclotron as a function of RF phase. This method is used
to evaluate the merits of various central geometries and injection energies.
This method is also used to examine the effects of flat-topping the RF
voltage by adding some third harmonic to the fundamental waveform. It is
found that addition of the optimum amount of third harmonic increases the
phase acceptance by about 20 deg. Finally, the effects of field bumps on
the axial motions are investigated.
To allow accurate radial motion calculations to high energy, an
approximate formula is developed which yields accurate (<1%) values for the
changes in orbit properties of an ion crossing a dee gap. The geometry of
the orbit on the first turn is discussed in detail. The radial centring is
studied by tracking ions from injection to 20 MeV, and a method is
described for choosing the starting conditions of the beam so as to minimize
the radial betatron amplitude over a desired phase range.
The problems associated with using a three-fold symmetric magnetic
field with a two-fold symmetric electric field are also discussed. Besides
the well-known gap-crossing resonance, a previously ignored phase-oscillation
effect is found to be important for cyclotrons operating on a
high harmonic of the ion rotation frequency.
UR - https://open.library.ubc.ca/collections/51833/items/1.0107853
ER - End of Reference