*Pisin Chen* `chen@slac.stanford.edu`

Stanfford Linear Accelerator Center

Stanford University, Stanford

CA
94309, USA3mm

When I first switched from theoretical particle physics to beam physics, one of my wonders was: Where is the ? The tone was a bit like the American slang "Where is the meat?", as if the real show was missing. Of course I quickly came to appreciate that the physics of complexity is just as interesting and exciting as the physics of simplicity. Besides, that first impression was only partially true: There is no lack of 's even in beam physics.

Before itemizing where the hides in beam physics, it should be
helpful to appreciate why in a physical system such as a high energy
beam interacting with cavities and magnetic components the is
largely absent. This should blame primarily on the special relativity.
As is well-known,
the quantum effects become important in a physical system when the
dimensions involved is of the order of the de Broglie wavelength,
, of the particles in the system, where *p* is the
particle momentum. For nonrelativistic particles is of the
order Compton wavelength,
cm or larger. For relativistic particles is suppressed by
the Lorentz factor and clearly is much too small compared with the
typical aperture of the cavities and components in accelerators. It is
thus clear that the primary effects in beam dynamics is essentially
classical, which is opposite to another collective system, namely the
condensed matter. High energy particles do interact quantum mechanically.
But that requires particles to be very close to each other accordingly.
That, however, is in the domain of high energy particle physics.

Having this said, we understand that most quantum effects that are involved in beam physics is through the ``secondary" effects due to electron-photon interactions, which are typically a factor fine structure constant, , smaller than the primary effects such as the classical particle motion. This is not to say, however, that these effects are relatively unimportant, as accelerator performance typically demands super-high precisions. Among this catalogy we can think of the issues of quantum fluctuations due to synchrotron radiation in storage rings, due to undulator radiation in FEL's, and the Sokolov-Ternov effect of spin polarization as a consequence of synchrotron radiation. These are already part of the standard knowledge in beam physics.

In reponse to the continued demand for higher energy, lower emittance, higher brightness beams, there also emerges a new class of beam phenomena which involve quantum mechanics. This is mainly through the applications of laser in various concepts of beam cooling and monitoring. One can readily think of the ideas of beam stochastic cooling using laser as the probe[1], three dimensional laser cooling of electron beams[3], laser cooling of bunched beams in storage rings[2], and beam cooling by Compton scattering using laser[4], etc. The laser interfereometry[5] and the laser ``wire" approaches to beam monitoring again necessarily involve beam-laser interaction. Compton or Thomson backscatterings[6] have also been invoked as a means to provide high brightness, beyond x-ray, light sources.

In a very different corner from beam production and handling, at the
interaction point of linear colliders there is, for the first time in
beam physics, indeed a quantum effect named
*beamstrahlung*[7]
which becomes comparably pronounced to its primary classical effect
*disruption*. (This time due to special relativity). Because the
very high energy electron-positron beams collide each other head-on,
in the rest frame of one beam the particles experience a very
intense electromagnetic field of the oncoming beam which is enhanced by
a Lorentz factor relative to that in the lab frame.
This field is so strong in most of the next generation
linear colliders that is comparable to the magnetic field strength
on the surface of a neutron star, or Gauss. In the farther
future even higher energy linear colliders call for such a beam field
which is way exceeding the Schwinger critical field strength, Gauss. Under such a condition
the vacuum is becoming so unrest that pairs can emerge from it.
In the context of beamstrahlung this phenomenon has been called
*coherent pair creation*[8]. On the theoretical side, this
quantum phenomenon is in the domain of what is called ``nonlinear quantum
electrodynamics". On the practical side, these pairs imposes constraints
on the detector and collider designs. Thus for the first time a beam
physics issue requires the joint effort among particle theorists,
experimentalists, and beam physicists, rightfully at the intersection
among the three branches of high energy physics.

There is yet another way where quantum mechanics is associated with beam physics, nothing to do with , however. There have been attempts to apply the theoretical concepts or the mathematical frame work developed in quantum mechanics (here we use the word in a broad sense to include also quantum field theory) for the study of beam dynamics. For example, there has been the effort of developing a renormalized theory for bram-beam interaction[11], inspired by the formalism of perturbative quantum field theories. There has also been an effort to treat the beam phase space transport in terms of a Schrodinger-like equation, with the normalized emittance playing the role of [9]. Photon beam propagation can in principle be described in terms of the Wigner function[10]. Most recently, there is also the thought of beam phenomena which are related to supersymmetry (in essense)[12]. If one insists, one can argue that the Lie algebra approach to beam optics also has some ``quantum flavor".

Looking at these developments, we see that quantum aspects plays more and more important roles in beam physics as the demand in the field points to ever higher energy, lower emittance, or higher brightness beams. It should be timely that we put more attention to its progresses and challenges.