Advanced Accelerators       updated October 25, 2007  D. Carrigan carrigan@fnal.gov (subject line must be sensible)

Channeling Formulary

Fermilab
 Home
 Pillars
 Channel Home
Infrared/Dyson
 SETI Biography Bibliography Nobel Prizes

Exotic Accelerators

Modern accelerators have been able to reach extremely high energies but at a cost. With available technology they must be very large and expensive to reach the ever-rising energy frontier. Currently they are limited by available magnetic fields, roughly 10 Tesla, and by RF gradients, at best 100 MeV/m.There are several possibilities for breaking the acceleration bottleneck. The first thought is to use the fantastic capabilities of lasers directly. A second possibility is to use a plasma wave to accelerate particles.

 

Plasma acceleration

In wakefield acceleration a laser or electron beam driver creates a moving wave in a plasma. In turn that wave accelerates a charged particle. The wake surfer illustrates a metaphor for the plasma wakefield acceleration process. In this illustration the wake driver is a powerful motorboat. The particle, here a surfboarder, is pushed along by the wave. Notice that the surfer is not connected to the boat by a rope. Phase stability is important. If the surfer drifts too far down the wave he no longer moves forward. He can accelerate for a while by moving up the wave. The plasma wakefield acceleration process is very similar to the metaphor.

The gradient, G, in a plasma is equal to 0.96*sqrt(n)
where n  is the electron density (per cm3) and G  is in V/cm. For a good electron plasma in a gas the density might reach 1018/cm2 and produce a gradient of 1 GV/cm. For a solid the density could be 10,000 times higher corresponding to 100 GV/cm.

 wake skier courtesy L. and S. Carrigan
Wake surfer (courtesy of L. and S. Carrigan)

Laser acceleration

The good news about lasers is that they can give very high electric fields. The bad news is that the electric vectors point in the wrong direction (transverse to the laser beam direction) and optical frequencies make the construction of an electromagnetic cavity outside of the reach of conventional technology. Several ingenious ideas have been advanced to overcome this problem including the use of gratings, exotic boundary conditions at metallic surfaces, and other special modes. In the last several years there has been some real progress on this at the STELLA facility at Brookhaven. STELLA was built to investigate the challenges of cascading laser staging. A powerful laser system is required for STELLA with 24 MW instantaneous for the first stage and 300 MW for the second. Initially this device has been used to demonstrate rephasing but not acceleration.

A large-scale laser accelerator R&D program, LEAP, is now underway at Stanford/SLAC

Solid State accelerators

 

Robert Hofstadter (Stanford HEPL-560-1968) mused on the limitations of conventional accelerators and speculated on an early version of a channeling accelerator. In his words "To anyone who has carried out experiments with a large modern accelerator there always comes a moment when he wishes that a powerful spatial compression of his equipment could take place.  If only the very large and massive pieces could fit in a small room!”  What Hofstadter imagined was a tabletop accelerator he called Miniac. The device would consist of a single crystal driven by an x-ray laser. Channeling would be used to focus the beam. Hofstadter realized the device might be an after-burner to boost a conventional accelerator beam that was already up into the relativistic regime somewhat in the spirit of the recent SLAC studies. At the time channeling was a new subject and x-ray lasers were distant dreams.

The basic solid-state acceleration paradigm is to excite a plasma wakefield in a crystal with a density thousands of time higher than a gas plasma. This possibility has been explored in some detail by Chen and Noble Relativistic Channeling (Carrigan and Ellison, eds) and Chen and Noble, p. 273 in Advanced Accelerator Concepts, eds. S. Chattopadhyay, et al., Amer. Inst. of Physics Press C398 (1997). Recent developments in femtosecond laser and electron beam technology make this possibility thinkable.

Pseudo solid state accelerators

In the last years there has been progress on something that might at first glance be considered solid-state acceleration. Groups from Livermore, Michigan, Rutherford and LULI have all seen energetic ions and electrons emanating from thin foils struck by extremely powerful picosecond laser pulses. At Livermore they observe “beams” of 1013 protons downstream of a foil irradiated with a 1000 TW, 3*1020 W/cm2 laser pulse. A beam can be focused by curving the foils. The high-energy ions originate from deposits or contaminants on the downstream side of the foil. The accelerating electrostatic field at the downstream surface is produced by ponderomotively accelerated hot electrons generated by the laser pulse. While this is an interesting process it should probably not be considered a solid-state accelerator since the electrostatic field is outside the solid.

What happens to a crystal exposed to the intense radiation needed to create a plasma wakefield? An electronic plasma excited by tunnel ionization decays via electronic interband transitions with plasma lifetimes in the femtosecond range. The hot electron gas excites phonons in the lattice leading to crystal disorder, fracture, or vaporization.  At Livermore hydrodynamic heating occurs in the 1 to 10 ps range. These times are short but not so short that one can discount the possibility of plasma acceleration.

Channeling for crystal accelerators

In a crystal accelerator channeling would be used to reduce energy loss, to focus the particles, and perhaps even cool the beam. However there are significant problems. The required electron or laser driver beam is so powerful that the crystal would probably be blown away. In addition there is the classical problem of dechanneling where the channeled particle is scattered out of the channel. Interestingly, models of "dynamic channeling" suggest crystals may channel until they vaporize.

In the late 1990s Helen Edwards’ group at Fermilab built a prototype photoinjector at A0 to work on development of the Tesla injector (Tesla has now become part of the (International Linear Collider). The Tesla photoinjector is basically a gigantic photocathode powered by a laser and followed by warm and cold RF stations. The accelerator can deliver very large 14 MeV picosecond electron pulses on the order of 10 nanocoulombs or 105 A/cm2.

The Fermilab A0 photoinjector offered a means to probe in the direction of channeling conditions characteristic of those needed for solid-state acceleration and do observations of channeling under conditions never studied before. With the facility it was possible to study channeling behavior as the bunch charge increased and go several orders of magnitudes beyond earlier measurements. Our Darmsatdt-Fermilab group has used A0 to study channeling at the highest bunch charges ever channeling at the highest bunch charge ever.