Download Introduction Calculate the Stem Dimension Calculate the

In this paper, explained the process of calculation and design of cyclotron proton accelerator cavity and effects of cavity’s fundamental parts for tuning the frequency to
produce radioactive isotope FDG (FluoroDeoxyGlucose) using in PET imaging system. Rf cavity in 71 MHz resonant frequency is designed to accelerate the ions with an
energy output of 10 MeV. It should be small cyclotron to be installed in hospitals to produce FDG. System design process with high quality factor and small size, require to
optimize the different parts of RF system. The optimization of this system have been done at frequency of 71 MHz by HFSS and CST software and compared with each
other. And also the thermal consideration are examined.
Introduction
Most numerous of circular accelerators, cyclotrons are characterized by
magnetic field and accelerating RF frequency which are constant in time.
The Dees are driven by an RF voltage whose frequency matches the
constant cyclotron frequency f =qB/2πm of non-relativistic ions. Ions
from a central ion source are repetitively accelerated in and out of the
Dees on a spiral path to maximum energy. In practice, the magnetic field
must decrease with r to assure stability in the axial direction, and the
accelerating voltage must be high for ions to reach the design energy
before they get out of the accelerating phase of the RF cycle.
Ions from a central ion source are repetitively accelerated in and out of the
Dees on a spiral path to maximum energy.
In practice, the magnetic field must decrease with r to assure stability in the
axial direction, and the accelerating voltage must be high for
ions to reach the design energy.
Large energy gain per turn and change of voltage
values with energy, during the passage of the four
gap in each round will be earn for 60 or 80 round
as follow;
∆T=(10MeV-30keV)/(4×60{80})
= 41514.6{31156.25}
V=∆T/(τ sin(hα/2) sinφ) = 42.36kV
{31.8kV}
The maximum electric field
achievable is limited by a process
known as RF breakdown which
is known as the Kilpatrick Limit.
frf=1.64E2ke-8.5/Ek
According to our RF frequency,
71MHz, Kilpatrick limit will be;
Ek = 10.05 MV/m
And so Es as the maximum surface
electric field level is obtained as
follows;
Es=15.075 MV/m
Therefore, The minimum distance
between Dee and Liner to prevent
electric spark will be;
dmin =3.316mm
Calculate the Stem Dimension
Total Stems length is considered λ/2. So due to the design frequency
it will be calculated.
Also, the set of Stem and Liner will be considered as a coaxial cable
with the desired impedance. So diameter of Stems could be
determined by this approach. In the fact, Stem plays the role of inner
conductor and the Liner as an outer conductor. This means that for a
50ohm specific impedance, the Liner to Stem diameter should be
equal to 2/3. Hence, Stem diameter was estimated with this
phrase. Liner diameter, size of the magnet and
valley dimension are related to each other .
This research, explain the process of calculation
and design of H- ion accelerator cyclotron cavity
to produce radioactive isotope FDG using in PET
imaging system. H- ion in 71MHz resonant
frequency of the cavity is designed to accelerate
the ions with an 10 Mev energy.
Calculate the Dee Dimension
Particle should obtain energy equal to10MeV during the 60 to 80 revolution. As a sample, for 80
revolution, Dee angle will be calculated accurately as follow. The obtained particle energy through
the four Gap is:
E=4q VDee Sin( h/2 θDee), h=4
The energy gained by the particle in each round:
10Mv/80=125000=4 VDee Sin( h/2 θDee)
If VDee =50kV  Sin(2 θDee)=0.625  2 θDee =79.32  θDee =39.66°
And also, for 60 revolution, the energy gained by the particle in each round:
10Mv/60=166.6kv =4q VDee Sin( 2 θDee)= 166666.6
If VDee =50kv  Sin(2 θDee)=0.833  2 θDee =56.4  θDee =28.2°
And if VDee =42kv  Sin(2 θDee)=0.992  2 θDee =82.74  θDee =41.3°
Conclusion
This paper explain the general principles of the cyclotron
accelerator RF system and specially consider the Dee
angle and Stem-Liner distance effect to achieve desired
energy, 10MeV. The results illustrate that the RF power
transmit with minimum loss.
Specifications of system
Therefore, in our design θDee should be about 40° for VDee about 40kV .
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