Medidas de protección

Linac Development

The first stage of the project is the development of a test cavity. In this work a booster linac is designed to upgrade an existing cyclotron facility to a cyclinac in a compact space thanks to advances in high gradient technology. The RF optimisation of the accelerating cavity is presented in this thesis along with particle tracking results and the mechanical engineering design. The RF cavity design and

1. The Project: ProBE 17

Fig. 1.17 Artist’s Impression of The Christie Rutherford proton Centre [68].

fabrication was heavily influenced by the results obtained from the CLIC high gradient test programme [? ] at CERN to ensure the most reliable high gradient

operation. A beam dynamics study is also presented determining the best solution for adequate transmission through the linac. When fabrication of the cavity is complete it is foreseen to be conditioned and tested in the CLIC S-band high gradient test facility at CERN known as S-Box.

Linac Testing

Once the cavity testing is complete, the linac testing stage of the project can commence. As is shown in Figure 1.20 the fourth gantry room will be constructed at the same time as the rest of the facility, but patient treatment equipment will not be installed. Instead this room will become a research beam line with a length of around 10 metres. Here it will be possible to test the ProBE cavity with the real clinical beam. There will also be the capability at the Christie to test pCT detectors and conduct radio-biology amongst other research.

Superconducting Gantry

The third stage of the project is concerning beam delivery. Beam rigidity is defined as R= Bρ= p/q where B is the magnetic field, ρis the gyroradius of the particle

due to this field, p is the particle momentum, and q is it’s charge. At the high

energies necessary for proton imaging, beam rigidity is increased from 2.43 Tm at

250 MeV to 2.84 Tm at 350 MeV. Stronger magnets are necessary to manipulate

the beam around the patient in the same amount of space. The fourth treatment room at the Christie hospital is sized for a 250 MeV treatment gantry, so in the

18 1. The Project: ProBE

Fig. 1.18 The Varian Probeam multi-room proton therapy system. The fourth treatment room (right) at the Christie will have a superconducting gantry if they upgrade to higher energy protons [69].

same space superconducting magnets will be necessary. A preliminary design shown in Figure 1.21 satisfies the key requirements of the gantry but there are further improvements to be made and research to reduce the size of the achromats is ongoing, alongside beam tracking studies and inclusion of the booster linac into the final gantry design [74].

1. The Project: ProBE 19

Fig. 1.19 The Varian Probeam 253 MeV cyclotron being delivered at the Christie [70].

Fig. 1.20 Layout of the proton therapy facility at The Christie Hospital. Four treatment rooms can be seen on the blueprint. Initially the first 3 treatment rooms will be operational using the 253 MeV cyclotron as a proton source for treatment. During this time the fourth room will remain a research room with the clinical beam. The ProBE linac will be developed simultaneously and tested in the research room. Afterwards that the linac will move into the beam line, and the fourth treatment room may be upgraded to a superconducting gantry for pCT [73].

20 1. The Project: ProBE

Fig. 1.21 Top:Preliminary layout of the compact pCT gantry design; dipoles shown (curved) in black, quadrupoles shown in red. Bottom: visualisation inside the

Chapter 2

RF Particle Acceleration

In this chapter, the theory of RF particle acceleration is introduced. The theory of RF cavities and the interaction of charged particles is presented, alongside important figures of merit to consider when designing RF cavities. Various RF cavity structures, specifically the current landscape of low/medium-β structures,

are described alongside RF breakdown phenomenology and other high gradient (HG) limitations. The Lorentz force law

F=q(E+v×B) (2.1)

is the most important equation in accelerator physics. It shows that electromagnetic fields can be used to accelerate and manipulate charged particles. It describes the force (F) of an electromagnetic field on charged particleq [75]. In the presence of an

electric field (E), a charged particleq will be accelerated in the direction of motion

of that electric field, therefore gaining energy. The force F is perpendicular to

both the magnetic field (B) and the particle velocity (v). Hence, the magnetic field

component does not increase the energy of the particle but adds a component of motion transverse to the initial direction of motion, bending the particle’s trajectory. It is because of this we can use electromagnetic fields to manipulate and accelerate charged particle beams for their desired use.

2.1

RF Cavities

A particle accelerator is made up of one or more RF cavities. An RF cavity is a hollow metallic structure that can be filled with electromagnetic fields, by an external high-frequency power source. The fields that exist inside a cylindrical cavity are given by

∇2− 1 c δ2 δt !   E B    = 0. (2.2)

22 2. RF Particle Acceleration

Transverse Electro Magnetic (TEM) waves are not possible inside an RF pillbox cavity because to satisfy the boundary conditions either the electric or the magnetic field components must be in the direction of propagation. Assuming the cavity wall is a perfect electric conductor, the boundary condition is

Ez|Rcav = 0

for a Transverse Magnetic (TM) mode, and the magnetic field component is zero in the direction of propagation

Bz = 0.

For a Transverse Electric (TE) mode, the boundary condition is

δBz δn _R cav = 0

where δ/δn is normal to a point on the surface and the electric field component is

zero in the direction of propagation [76]

Ez = 0.

Fig. 2.1 Electric (E) and magnetic (B) fields for the transverse-magnetic resonant

TM010 mode in a cylindrical cavity [77].

Figure 2.1 shows the transverse-magnetic resonant mode (TM010) inside of a

cylindrical ‘pillbox’ cavity. The subscripts in TMmnp and TEmnp indicate different

mode patterns. In a rectangular cavity, m and n indicate the number of horizontal

periods and vertical periods respectively, and p is the number of longitudinal

periods in the direction of propagation. In a cylindrical cavity, m is the number

of full period variations of that field component in θ. n is the number of zeros of

2.1 RF Cavities 23

is the cavity radius and excluding r = 0. p once again indicates the number of

longitudinal periods in the direction of propagation. The analytical solution for the field components of the TM mode inside a pillbox cavity is given in terms of Bessel functions Ez =E0Jm(kmnr) cos(mθ) cos pπz l e jωt _(2.3a) Er =− pπ l a xmn E₀J_m′ (kmnr) cos(mθ) sin pπz l e jωt _(2.3b) Eθ =− pπ l ma2 x2_mnrE0Jm(kmnr) sin(mθ) sin pπz l e jωt _(2.3c) Bz = 0 (2.3d) Br =−jω ma2 x2_mnrc2E0Jm(Kmnr) sin(mθ) cos pπz l e jωt _(2.3e) Bθ =−jω a xmnc2 E₀J_m′ (Kmnr) cos(mθ) cos pπz l e jωt _(2.3f)

where E₀ is the electric field on the z-axis which is always the direction of

propagation in this work, and l is the length of a one cell pillbox cavity.

The TM010 mode is effective in particle acceleration because the particle beam

travels along the z-axis in the same direction as the electric field; it should also travel at the correct velocity to ensure the particle only sees the accelerating part of the wave, as is shown in Figure 2.2. If the bunch were to arrive at the wrong phase (ϕ), and see the decelerating part of the wave, it is not accelerated. When

synchronising the RF fields and the beam in time, we define a virtual particle called the synchronous particle (ϑs). Particles in the bunch that are faster or slower than

ϑs will see a different accelerating force.

Fig. 2.2 Beam bunches in the positive phase of an RF voltage [77].