An accelerator can circulate a lot of different particles, provided that they have an electric charge so that they can be accelerated with an electromagnetic field. The CERN accelerator complex accelerates protons, but also nuclei of ionized atoms ions , such as the nuclei of lead, argon or xenon atoms.
Some LHC runs are thus dedicated to lead-ion collisions. The energy of a particle is measured in electronvolts. One electronvolt is the energy gained by an electron that accelerates through a one-volt electrical field.
As they race around the LHC, the protons acquire an energy of 6. It is the highest energy reached by an accelerator, but in everyday terms, this is a ridiculously tiny energy; roughly the energy of a safety pin dropped from a height of just two centimetres. But an accelerator concentrates that energy at the infinitesimal scale to obtain very high concentrations of energy close to those that existed just after the Big Bang.
The instantaneous luminosity is expressed in cm -2 s -1 and the integrated luminosity, corresponding to the number of collisions that can occur over a given period, is measured in inverse femtobarn. One inverse femtobarn corresponds to million millions potential collisions. CERN operates a complex of eight accelerators and two decelerators. These accelerators supply experiments or are used as injectors, accelerating particles for larger accelerators. Some, such as the Proton Synchrotron PS or Super Proton Synchrotron SPS do both at once, preparing particles for experiments that they supply directly and injecting into larger accelerators.
The Large Hadron Collider is supplied with protons by a chain of four accelerators that boost the particles and divide them into bunches. Imagining, developing and building an accelerator takes several decades. For example, the former LEP electron-positron accelerator had not even begun operation when CERN scientists were already imagining replacing it with a more powerful accelerator.
That was in , twenty-four years before the LHC started. Work is also being done on alternative acceleration techniques for example with the AWAKE experiment. Many accelerators developed several decades ago are still in operation. The oldest of these is the Proton Synchrotron PS , commissioned in Others have been closed down, with some of their components being reused for new machines, at CERN or elsewhere.
Travel back into the past of CERN accelerators. Accelerators CERN hosts a gigantic complex of particle accelerators. What is an accelerator? Based on this and Figure , we can derive the period of motion as. If the velocity is not perpendicular to the magnetic field, then we can compare each component of the velocity separately with the magnetic field.
The component of the velocity perpendicular to the magnetic field produces a magnetic force perpendicular to both this velocity and the field:. The component parallel to the magnetic field creates constant motion along the same direction as the magnetic field, also shown in Figure. The parallel motion determines the pitch p of the helix, which is the distance between adjacent turns.
This distance equals the parallel component of the velocity times the period:. The result is a helical motion , as shown in the following figure. While the charged particle travels in a helical path, it may enter a region where the magnetic field is not uniform.
In particular, suppose a particle travels from a region of strong magnetic field to a region of weaker field, then back to a region of stronger field. The particle may reflect back before entering the stronger magnetic field region. This is similar to a wave on a string traveling from a very light, thin string to a hard wall and reflecting backward.
If the reflection happens at both ends, the particle is trapped in a so-called magnetic bottle. These belts were discovered by James Van Allen while trying to measure the flux of cosmic rays on Earth high-energy particles that come from outside the solar system to see whether this was similar to the flux measured on Earth. Aurorae , like the famous aurora borealis northern lights in the Northern Hemisphere Figure , are beautiful displays of light emitted as ions recombine with electrons entering the atmosphere as they spiral along magnetic field lines.
Aurorae have also been observed on other planets, such as Jupiter and Saturn. Beam Deflector A research group is investigating short-lived radioactive isotopes. They need to design a way to transport alpha-particles helium nuclei from where they are made to a place where they will collide with another material to form an isotope. The beam of alpha-particles bends through a degree region with a uniform magnetic field of 0.
Because the particle is only going around a quarter of a circle, we can take 0. However, for the given problem, the alpha-particle goes around a quarter of the circle, so the time it takes would be. Significance This time may be quick enough to get to the material we would like to bombard, depending on how short-lived the radioactive isotope is and continues to emit alpha-particles.
If we could increase the magnetic field applied in the region, this would shorten the time even more. The path the particles need to take could be shortened, but this may not be economical given the experimental setup. Check Your Understanding A uniform magnetic field of magnitude 1. Helical Motion in a Magnetic Field A proton enters a uniform magnetic field of with a speed of At what angle must the magnetic field be from the velocity so that the pitch of the resulting helical motion is equal to the radius of the helix?
Strategy The pitch of the motion relates to the parallel velocity times the period of the circular motion, whereas the radius relates to the perpendicular velocity component. After setting the radius and the pitch equal to each other, solve for the angle between the magnetic field and velocity or. Solution The pitch is given by Figure , the period is given by Figure , and the radius of circular motion is given by Figure.
Note that the velocity in the radius equation is related to only the perpendicular velocity, which is where the circular motion occurs. Ion acceleration with high-intensity lasers has attracted a great deal of attention because accelerated ion beams have extreme laminarity, ultrashort duration and high particle number in MeV energy range.
These phenomenal characteristics of ion beam prompted excogitation about a wide range of applications in nuclear and medicine physics 1 , 2 , 3. The requirement of ion beam with narrow energy spread, high conversion efficiency and compatibility of target with the high-repetition rate laser system, still a challenging task despite a decade plus efforts 4.
The widely employed schemes for laser driven ion acceleration include target normal sheath acceleration TNSA 5 , 6 , 7 , radiation pressure acceleration RPA 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , breakout afterburner BOA 17 , collisionless shockwave acceleration CSA 18 , 19 , 20 and magnetic vortex acceleration MVA 21 , 22 , 23 , The most stable and well-understood mechanism so far is the TNSA 5 , 6 , 7 , which usually requires long pulse duration in order to reach high cut-off energy and thin solid target which allows us to get very sharp density gradients and high accelerating fields.
At high repetition rate, using such targets raises significant challenges with debris, target insertion and unwanted secondary radiation such as bremsstrahlung. In comparison to typical ion acceleration experiments which utilizes a laser-thin solid foil interaction; MVA in near critical density NCD plasmas may be realized in a high density gas jet 25 which are considered to have an advantage of higher laser-plasma coupling.
The use of NCD target allows the MVA mechanism to generate high-energy ions at high repetition from a high purity proton source, which is attractive for applications required high repetition rate with the solid-state lasers. Recently MVA mechanism, employing the NCD target interaction with the linearly polarized LP laser pulses has been investigated theoretically 21 , 22 , 23 , 24 and experimentally 26 , 27 and attracted a great deal of attention due to its prediction for achieving sub-relativistic to relativistic electron and proton source.
It has been recognized that gas jet targets offer the possibility for high repetition rates 28 , 29 , however their performance as proton sources has been limited to low particle energies and yields For the detailed review of laser-driven ion acceleration see refs 4 , In this work, we focused on the aspect of efficient proton acceleration from MVA mechanism where we have used the circularly polarized CP laser pulse interaction with NCD plasma target.
So far, there is less attention paid to CP laser driven MVA mechanism and subsequently on efficient generation of electron and proton beam, which is needed, for applications. However intense CP laser interaction with plasma channels has shown great potential for the generation of megagauss axial magnetic field 32 which has both fundamental and application interest such as particle acceleration and collimation.
The preference of CP over LP laser pulse enabled the generation of axial and azimuthal magnetic fields in plasma channel. This new insight of polarization dependence in MVA mechanism of ion acceleration, has resulted the generation of quasi-monoenergetic helical electron beam and high energy quasi-monoenergetic proton beam with high proton yields.
MVA mechanism 22 of ion acceleration can be realized when the laser pulse propagates through a NCD target that is much longer than the laser pulse itself. As tightly focused laser pulse interacts with the target, the ponderomotive force of the laser pulse drives electron cavitation.
Plasma electrons become trapped and accelerated within these cavitation. These fast electrons trail behind the laser front, forming an axial fast current. A cold electron return current is formed to balance the fast current to maintain the plasma quasi-neutrality. Upon exiting the channel, the magnetic field expands into vacuum and the electron current is dissipated.
This field has the form of a dipole in 2D and a toroidal vortex in 3D. The magnetic field displaces the electron component of plasma with regard to the ion component and a strong quasi-static electric field is generated at rear side of plasma target which accelerate and collimate the ion beam to achieve higher energies. The effectiveness of this mechanism depends on the efficient transfer of laser pulse energy into the energy of fast electrons that are accelerated along the laser propagation direction.
Thus in MVA mechanism for each laser target configuration there exists an optimum target thickness that maximizes the ion energy. We extended further the MVA ion acceleration in non-uniform plasma and demonstrated the role of density scale length at rear side of plasma-vacuum interface on ion acceleration.
The results highlighted the fact that high-energy ion acceleration can be realised in experiment by using the near-critical density target with optimum plasma thickness and by controlling the laser beam parameter. The schematic of CP laser interaction with the target is shown in Fig. The plasma target considered in this simulation study is uniform and non-uniform both. For optimum acceleration in case of MVA 23 , the laser spot size should match the size of the self-focusing channel in order to avoid filamentation.
Blue spiral curve shows the generation of helical relativistic electron beam from MVA mechanism. The effectiveness of MVA mechanism requires the efficient transfer of laser energy to the fast electrons in the plasma, which are accelerated in the plasma channel along the laser propagation direction. We begin by performing the simulation for the idealized case of plasma target — that is, with sharp plasma-vacuum interface — and CP laser.
Detailed simulation parameters can be found in the Methods. We show in Fig. By this time the laser pulse has been passed through the NCD plasma target and, has formed a channel from which the electrons and ions are expelled preferentially in the transverse direction to the laser propagation direction.
Color bars show the variation in electron and ion charge density. The most interesting point here is the observation of relativistic electron beam of helical shape in vacuum at rear side of plasma target. To understand the formation of helical shape electron beam, we followed the interaction of focused laser pulse in underdense plasma channel, which generates the axial and azimuthal magnetic field Axial B y and azimuthal magnetic field B z can be written as respectively,.
The expression for axial magnetic field B y as given by Eq. The azimuthal magnetic field given by Eq. Consequently a symmetric, tightly focused laser will tend to eject ring of electrons modulated in helical shape as shown by Fig. We show here in Fig. Helical electron beam shown in red shows the ring structures with negligible axial current. The contour plot shown in Fig. Figure 3b shows the electron energy distribution at time instant, after depleted laser pulse exits from the rear side of plasma and maximum acceleration is achieved.
The energy spectrum of electron beam shows the quasi-monoenergetic feature due to CP laser, which is different from typical thermal energy distribution. More interestingly mono-energetic feature is traced on energy distribution of proton beam depicted later for proton beam characteristics. The energy density distribution in Fig. Helical shaped high-energy electron beam 34 , 35 with quasi-monoenergetic nature may be used for plasma based X-ray source and collimation of positron beam source.
Simulation Results on generation of helical shaped high-energy electron beam from MVA mechanism has shown resemblance with the previous experiment and simulation study 35 where relativistic energy electron rings were observed from laser wakefield acceleration experiments in the blowout regime.
The ring produced in both the experiment and simulation were accompanied by substantial axial current making it impractical; to utilise these rings for applications the ratio of the ring to axial current must be increased. In this report, we find that magnetic vortex field at the rear side of target prevents the flow of axial electron current resulting in hollow electron beam of helical shaped rings.
The results shown in Figs 2 a and 3 a for electron charge density and current distribution illustrates this feature where axial electrons are stopped due to magnetic field and helical shaped hollow electron rings can be seen propagating in vacuum. The energy density of electrons are normalised with n c m e c 2. The simulation results shown are for laser — plasma parameters as shown in Fig. As shown previously Figs 2a — 3a that high-energy electrons are localised along the centre axis of channel and a fraction of them are accelerated in forward direction, which trail behind the laser front, forming an axial fast current.
To maintain plasma quasi-neutrality, a cold electron return current is formed to balance the fast current. Thus, background electrons flow outside the channel forming a return current. It can be seen from Fig. Its evident from Fig. In case of homogenous plasma at plasma — vacuum interface, the abrupt decrease in magnetic field induces a strong electric field, which is responsible to accelerate the ion beam to high energies.
The simulation result shown are for laser — plasma parameters as shown in Fig. X-axis and Y-axis are in micron and colour bar shows the variation in current density.
It is found from the analytical estimation that axial magnetic field is peaked near the laser axis i. Figure 5a, b shows spatial and temporal evolution of azimuthal and axial magnetic field at time instant when laser pulse exits the rear side of target.
As shown in Fig. The transverse and longitudinal expansion of azimuthal magnetic field leads to the decrease of electrons drift speed, which are coming out from the plasma channel. Thus the slowdown of electron speed increases the density locally and hence the current distribution at rear side of target. In our study the transverse and longitudinal expansion of azimuthal magnetic field shown by Fig. Figure 6b shows the variation of transverse focusing field, which is responsible for ion beam focusing towards the propagation axis.
We illustrated the MVA mechanism as depicted in Figs 2 — 6 which relies on self-generated quasi-static magnetic field Fig. Here in CP laser pulses driven MVA, we have shown that magnetic pressure expels electrons from the magnetic region into the plasma channel and builds up an electrostatics field, which accelerates the ions in laser propagation direction at plasma-vacuum interface.
We depicted the proton energy distribution in Fig. Further the proton beam is characterised as shown in Fig. Figure 7c shows the spatial density distribution of focused proton beam where high-energy protons are concentrated in very small area; which can be attributed to transverse focusing field as shown in Fig.
Figure 7 d,e shows the angular distribution of proton beam, which clearly demonstrates that high-energy protons are collimated at smaller divergence angle. The angular distribution of protons is shown by d , e.
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