At the end of this era of radiation, we entered the era of matter, relating to the formation of the nucleus (180 s) with decoupling matter-radiation, succeeded by forming atoms (300,000 years), and the universe became transparent. Finally, stars were formed (1 billion years) with the first supernova. Here, the formation of heavy atoms, protogalaxies, and black holes occurred. Approximately 13.7 billion years later is the present time, with the spiral galaxy and solar system, etc. [1]. Thus, after just 10−10 s from the Big Bang, protons were already formed.
For more information about the physics of the Big Bang related to hadron therapy, the reader is referred to the book Particle Accelerators: From Big Bang to Physics Hadron Therapy by Amaldi [2].
It is worth noting that only 5 % of the matter in the universe is visible matter (which is subject to the standard model). The rest is dark matter (20 %) and dark energy (75 %) [1], which does not apply this model (see Fig. 2.2). Our knowledge of the universe is minimal, but the advantage that the universe has over man—being immense and eternal—is not known to it because the universe does not think (as the French philosopher Pascal said).
2.1.2 Hadrons
The hadrons known to date are protons, neutrons, and a meson (pions). Pions are the most common types of particles in a particle collision and may be considered mild proton mass to approximately 15 % of that of the proton. There are two kinds of hadrons, classified according to their spins: baryons (half spin) and mesons (integer spin). Thus, the hadrons [1] are baryons (proton [p], neutron [n]) and mesons (pion π+, π− and πο)
Hadrons penetrate deeper than electrons and photons but not as deeply as muons and neutrinos. In general hadron therapy, it is considered as hadrons protons, neutrons, pions, ions (alpha, C, N). The hadrons are highly interactive particles experiencing strong force. Hadron therapy (HT) is radiation therapy that uses hadrons. The strength of HT lies in the physical and radiobiological properties unique to these particles; they can penetrate tissues with limited diffusion and deposit maximum energy just before stopping (Bragg peak). This allows a precisely defined region to be specifically irradiated. HT allows access to a more controlled distance than conventional radiotherapy; however, the patient cannot move during application so that the radiation does not harm healthy tissue. Thus, with the use of hadrons, the tumor can be irradiated with less damage to healthy tissue compared with X-ray [4, 5].
2.1.3 Evolution of Energy
When working with particle accelerators, smaller distances are tested for higher energy accelerated particles. In 1930, testing values for a distance of 10−11 m required about 100 keV. Twenty years later, approximately 100 MeV was reached with testing distances of 10−14 m. In 1970, 100 GeV was reached and distances up to 10−17 m could be tested; in 1990, 10−18 m was reached with energy of 1 TeV. Currently, 10 TeV in the large hadron collider (LHC) has reached 10−19 m. How much we will we be able to reach in the coming years as accelerators grow in size, complexity, and cost?
Figure 2.3 shows a sharp increase in power over time: an order of magnitude for every 6–10 years. Each generation replaces the previous for increasingly high energy. It is important to note that energy is not the only interesting parameter: consider also the intensity and size of the beam.
Fig. 2.3
A Livingston plot showing the evolution of accelerator laboratory energy from 1930 until 2005 [6]. The energy of colliders is plotted in terms of the laboratory energy of particles colliding with a proton at rest to reach the same center of mass energy. Courtesy Prof. Dr. Wolfgang Kurt Hermann “Pief” Panofsky
Protontherapy uses accelerators with energy around 200–250 MeV/u, whereas carbon ion therapy uses 400–450 MeV/u with a current of 0.1 nA [1]. Circular accelerators, such as the Cyclotron and Synchrotron, are the most frequently used. The Cyclinac (which is a combination between a linac and Cyclotron accelerator) and the Laser and dielectric wall accelerators (DWA) are in development; if successful, they will reduce the cost, size, and complexity of current accelerators. The largest particle accelerator in the world, the LHC, has a biomedical facility for advanced research and education, called Low Energy Ionizing Ring (LEIR; http://medicalphysicsweb.org/cws/article/opinion/56295) to study basic physical and radiobiology, carbon ion fragmentation, dosimetry, and test instrumentation.
All circular accelerators use a linear accelerator), which, by means of electrical fields generated by radiofrequency (RF) cavities accelerate particles, and the bending trajectory, and the focusing, made by magnets. For the LHC to preserve proton beams in a path of 27 km, the magnetic fields require constant adjustment to compensate for the beam energy increases. The magnetic fields are on the order of 8.3 T—in other words, 170,000 times stronger than the earth’s magnetic field. A field of this value requires a current of approximately 11,800 A. The 1232 magnets consume an electric current that could fill the needs of a small town with 150,000 houses!
Considering the LHC complex as a whole, the power consumption would be about 120 million watts of electrical power during peak demand [7]. The stored energy totals 11 billion joules—the amount of energy stored in 2.5 tons of TNT, spread over the 27 km. Each bending magnet of the trajectory of the protons is 14 m long and weighs 35 tons. The system temperature is maintained at −271 °C, requiring 10,800 tons of liquid nitrogen, followed by 120 tons of liquid helium (the cooling process takes a month and a half). The cables are made of an alloy of superconducting niobium-titanium. The length of the filaments used in bending magnets is equivalent to five times the distance from Earth to the sun and back, with plenty for any round trip around the moon (Don Lincoln). Thus, we can say that we have entered a golden age with new discoveries in all areas of human knowledge—physics, astronomy, chemistry, mathematics, computer simulation, industry, and others—through the creation of the LHC and the injection of $10 billion from participating nations in its construction.
Only with international integrated cooperation was it possible to build the LHC. With the additional experiments to be performed at the LHC, we believe that the importance may not be learning about elementary particles but to bring a deeper understanding of the fundamental questions about the universe. Finally, hadronic therapy will eventually move through physical and biophysical research; with the use of the LEIR of the European Organization for Nuclear Research (CERN), researchers will embrace new therapeutic approaches to save lives and cancer will be destroyed.
2.2 The Cyclotron, Ernest Orlando Lawrence, and Equations
The cyclotron was invented in 1932 by Ernest Lawrence. It accelerated protons with a fixed frequency of up to 1.25 MeV, allowing nuclear transmutation [8, 9]. Lawrence received the Nobel Prize 7 years later. The University of Berkeley recognized the potential of this new machine and built a 5-m-long cyclotron that accelerated protons to an energy of 20 MeV. Figure 2.4 shows two current cyclotrons and a schematic drawing in which the magnetic field imposes a circular path on the particles. The oscillating electric field (RF) is responsible for particle acceleration; the final trajectory is a spiral.
Fig. 2.4
a Commercial cyclotrons (Ion Beam Applications variants and the Varian Accelerator). b Schematic drawing of a cyclotron. Reproduced from [10]
2.2.1 Motion of Particles: Equations
The force acting on a particle, with velocity v in a magnetic field B, has the following characteristics. The direction is perpendicular to the plane (v, B); this can be represented by the lefthand rule where the thumb, index, and middle fingers are mutually perpendicular (90°). The thumb indicates the direction of the force, the index finger is the vector magnetic field, and the middle finger is the speed. The magnitude of the magnetic force that acts on the particle is given by f = qv Bsin ϕ, where f is the magnetic force, q is the particle charge in Coulombs, and ϕ is the angle between the vectors B and v (this angle can vary from 0 to 180°). This is explained in more detail in Fig. 2.5.
Furthermore, when observing the particles from a proton–proton collision, for example, it can be concluded that particles of lower energy bend more and higher energy particles bend less because the magnetic field can bend the path of a particle. Because the magnetic force depends on the active particle charge, the trajectory can curve in either direction. If v is perpendicular to B, the equality decreases to F = qvB. However, Newton’s equation gives the expression for the force F = mass (m) × acceleration (a), which means that to find the necessary replacements, the following equations are used for the speed and radius:
Because we know v, we can calculate the acceleration as a = v 2/r. Substituting the value of v in the equation, the acceleration is obtained. Because the radiated power is given by Pα (q 2 a 2/c 2)—that is, Pα (qB/m)4 r 2, it can be concluded that a smaller mass has greater radiated power, which causes the withdrawal of the beam particle. Thus, the electron radiates more power than the proton.
2.2.2 Calculating the Frequency of the Cyclotron
Calculation of the frequency of the cyclotron is very straightforward. The total turn is equal to 2πr in a path of radius r. If t is defined as the time spent in the half turn, v = πr/t, then t = πr/v. However, because v = qBr /m, then t = πm /qB. Thus, the time spent on the course is the same for all orbits, independent of the radius. Because the period of one complete turn (T) is twice that spent in the half turn T = 2t, then T = 2πm/qB. Because the frequency (ν) is the inverse of the period, we have ν = 1/T, and thus ν = qB /2πm. The angular frequency becomes ω = 2πν, then ω = qB/m.
This is the frequency value obtained from the RF source to produce the acceleration of a charged particle q and mass m, which are subjected to the magnetic field B. It can be concluded that the cyclotron frequency is directly proportional to B and inversely proportional to the ratio m/q. Thus, the particle with the lowest m/q ratio produces a spiral with more full turns (higher frequency), provided that the field remains constant.
A video on the cyclotron can be viewed at http://www.youtube.com/watch?v=cNnNM2ZqIsc.
If a cyclotron (200 MeV) were as small and inexpensive as the 5–20 MeV linacs used in conventional radiotherapy, then more than 90 % of patients could be treated with a proton beam. The accelerators used today are large and expensive, costing around 20 million Euros for a proton accelerator and 40 million Euros for a carbon ion beam facility. The installation of gantries would add another 10–12 million Euros to the cost. The gantry used at the Heidelberg Ion-Beam Therapy Center (HIT) weighs 670 tons and consumes 400 kW of power. Considering the LHC complex as a whole, the power consumption would be approximately 120 million watts of electrical power at peak demand. The stored energy is 11 billion joules (1). In the future, it is possible that gantries will be built using superconducting magnets. The current situation regarding size and costs is expected to change in the future. The Belgian company Ion Beam Applications (IBA) already offers a superconducting cyclotron with a 6 m diameter, which accelerates carbon ions up to 400 MeV/u. The TERA Foundation introduced and developed a new type of accelerator, the cyclinac [11], to accelerate protons and carbon ions, with a time of only 1 ms required to vary the energy of the beam, compared with the 20–50 ms needed by a cyclotron and the 1 s needed by a synchrotron.
2.3 The Proton Synchrotron, E.M. McMillan and V. Veskler
Conceptually, the principle of the synchrotron was published in a Russian newspaper by Vladimir Veksler; however, it was built by Edwin McMillan in 1945 (Fig. 2.6). The first proton synchrotron was designed by Sir Mark Oliphant, Australian physicist, and built in 1952 [12]. In particle physics, the synchrotron is an accelerator of cyclic particles in which the electric field is responsible for the acceleration of the particles and the magnetic field is responsible for the change of direction of the particles; both fields are synchronized with a beam of particles. The magnetic field is increased to keep the charged particles in a constant radius orbit as they reach higher speeds. Because the radius is constant, the “dees” used in the cyclotron are not needed and the particle moves in an annular chamber vacuum in a ring-shaped magnet. One or more resonant cavities are used to accelerate particles. An RF is applied into the cavity so that the particles are attracted when they approach and repelled when they leave it (Fig. 2.7).
Fig. 2.6
The Synchrotron. Courtesy Prof. Dr. Hans-H. Braun
Fig. 2.7
Layout of an early proton synchrotron and a system of coupled equations. A synchrotron can be built for very high energies. For proton beams, limits are given by achievable magnetic field and size. Courtesy Prof. Dr. Hans-H. Braun
The orbit of a synchrotron is not a circle; rather, straight sections are added by the RF cavities, injection, and extraction, etc. Usually, the pre-accelerated beam is a linac (or small synchrotron, prior to injection). The curvature of beam radius does not match the machine radius.
An interesting comparison was proposed by Don Lincoln in his book The Quantum Frontier [7], which facilitates an understanding of the functioning of a proton synchrotron. The principle governing this accelerator is the same as that governing a tetherball (i.e., a ball attached to one end of a rope, with the other end attached to the top of a tall pole that is anchored deep in the ground). A person hits the tetherball and the rope ensures that the ball travels in a circular path. Once the ball makes a full circle, it is hit again. The ball goes faster and makes another circuit. If the rope is attached to the top of the pole, it does not wrap itself around the pole; in principle, the ball can be made to travel very rapidly by synchronizing both its orbit and the person hitting it (hence the derivation of the name synchrotron). In a proton synchrotron, the electric field “hits” the proton and accelerates it. However, the counterpart of the rope in the tetherball analogy is not provided by electric fields, but rather by magnetic fields. Particles are accelerated by an electric field over a short distance and are then guided by magnetic fields in a circular path back to the electric field region for another round of acceleration.
The synchrotron was based on the cyclotron with a time-dependent magnetic guide, which was synchronized to a particle beam with increasing kinetic energy. The difference between the cyclotron and synchrotron is that the latter uses the principle of phase stability, maintaining the synchronism between the applied electric field and the frequency of revolution of the particle. Beam focusing and acceleration can be separated into different components using the curvature of the synchrotron beam. Thus, radiofrequency cavities are used for acceleration, the magnetic dipoles for particle deflection, and quadrupole/sextupole magnets for focusing the beam particles. The magnetic field maintains the orbit instead of accelerating the particles, and hence the magnetic field lines are only necessary in the region defined by the orbit.
The synchrotron facility consists of the following components (Fig. 2.8):
Fig. 2.8
a Synchrotron at the HIT in Heidelberg. b Schematic of the synchrotron at the HIT. c Schematic drawing of the HIT gantry. Courtesy Annette Tuffs, Head of Corporate Communications/Press Office, Heidelberg University Hospital
(1)
The ion source accelerator: This is where ion beams composed of positively charged atoms are produced. For protons, hydrogen gas is used. For carbon ions, dioxide is used.
(2)
A two-stage linear accelerator: Ions are accelerated in structures at high frequency up to 10 % of the speed of light.
(3)
The synchrotron: Six 60° magnets bend the ions into a circular path. After a million orbits, ions are accelerated to 75 % of the speed of light.
(4)
The treatment room beam lines: Magnets guide and focus the beam of ions in vacuum tubes.
(5)
The treatment room: The beam enters the treatment room through a window. The patient is positioned on a treatment table that is adjusted accurately by a computer-controlled robot.
(6)
Position control: Using a digital X-ray machine, images are obtained before irradiation. The computer software compares the images obtained with those used in treatment planning and precisely adjusts the position of the patient.
(7)
The gantry: The rotation system enables the beam to be directed toward the patient at an optimized angle. The gantry weighs about 670 tons—600 tons of which can be rotated with submillimeter accuracy.
(8)
The treatment room in the gantry: This is where the beam exits the gantry (beam line). Two rotation systems and digital X-rays are used to optimize the position of the patient guided by the images taken before irradiation.
The combination of magnetic field “guides”, time dependency, and the principle of strong focus enables the design and operation of modern large-scale accelerators as colliders and even synchrotron light sources, such as at the Brazilian Synchrotron Light Laboratory in Campinas, São Paulo. The power limit could be increased by using superconducting magnets, which are not limited by magnetic saturation. Electron and positron accelerators may be limited by the emission of synchrotron radiation, resulting in a partial loss of kinetic energy of the particle beam. Therefore, the energy of electron and positron accelerators is limited by the loss of this radiation, which does not happen with proton or ion accelerators. The energy of these accelerators is limited by the strength of the magnets and the cost.
In the synchrotron, particle injection is pre-accelerated using a linac, microtron, or even another synchrotron, because synchrotrons are unable to accelerate particles from zero kinetic energy. The Tevatron at Fermilab was the largest collider in the world in 2008. It accelerated protons and antiprotons to 1 TeV and then collided them. The LHC has seven times this energy; accordingly, the proton–proton collisions occur at about 14 TeV. The LHC also accelerates heavy ions (such as lead) up to an energy of 1.15 PeV [13].
2.4 Hybrid Systems: C400 from IBA and New Synchrotron from Brookhaven National Laboratory
The C400 from Ion Beam Applications (IBA, Belgium), is being developed in partnership with the Joint Institute for Nuclear Research (JINR, Dubna, Russia). It is a cyclotron with superconducting coils that can produce 400 MeV energy, allowing the acceleration of protons and carbon ions. This cyclotron follows the current trend in the development of systems for providing protontherapy and carbon ion therapy in the same equipment—that is, hybrid systems. However, despite the IBA having developed a compact gantry for ProteusOne, it does not have a similar system for the C400. The C400, shown in Figs. 2.9 and 2.10, has a diameter of 6.3 m; its estimated main parameters are provided in Table 2.1.
Fig. 2.9
Cyclotron C400 IBA. Courtesy IBA
Fig. 2.10
Cyclotron C400 IBA, about 6.3 m in diameter with superconducting coils. Courtesy IBA
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