Beam emittance

The emittance is the product of angular divergence and cross- sectional area of ​​a particle or the light beam. More specifically, the emittance indicated volume, filling a particle or ray of light in the phase space. The term is mainly used in electron optics and accelerator physics of meaning as a measure of cross-section and concentration of a particle beam in an accelerator.

Introduction

Considering first the particles of a particle beam that has been generated from a particle source: Under the assumption that the particles move nearly parallel to the positive z-axis, namely (for simplicity ) only in one plane, the xz-plane. Then, the phase space is two-dimensional, it is composed of the plane of the coordinates x and clamped px, px being the x-component of the particle (which is much smaller in this case than the z-component pz). Instead of the momentum component px θ can take advantage of the small angle which the direction of flight of the particle with the z- axis; we have: θ = px / pz, where θ in radians, is thus measured in radians ( 1 rad = 57.3 °).

Referring now to these x - θ plane at a given point z, then each particle is characterized by a point in this plane. All Teilchenpunkte are located in a certain region of the plane, that is, the phase space; the size of this area in the x- θ plane, the emittance, as measured, for example, in mm · mrad.

In practice, the particles of the beam are ( substantially in the z- direction of flying ), have not only an x-component, but also a y-component, the phase space is four-dimensional instead of two-dimensionally. Then the Teilchenpunkte do not fill an area, but a four-dimensional volume, measured in (mm mrad ) 2

Example: a parallel light beam in the z direction focused by a condenser lens onto a small focal spot, so the width of the beam is thereby reduced, but the angle of the individual beams to the z- axis is expanding: the product, the emittance remains constant. This is an example of the set of Liouville: in application of nonlinear optics is the emittance of a conserved quantity, that is, it does not change along the beam in the z- direction.

Applications

Emittance denotes the phase volume of an ensemble of particles, [Note 1] which has been generated, for example, by a particle, or which is in a particle accelerator. Emittance is determined by the properties of the (light or particles ) source. At high beam currents, i.e., an ensemble made ​​up of many charged particles, the electromagnetic interaction between the particles of the particle beam and can not be neglected. The space charge effects occurring thereby lead to an increase in the emittance. Also perform other nonlinear effects, such as loss of energy by friction or synchrotron radiation delivery to an increase in the emittance, ie, the emittance is then not conserved. Also, in the acceleration of the particles in the beam direction, the emittance changing. It is smaller, since the longitudinal component of the momentum vector increases during acceleration, the transverse components but does not change the divergence of the beam becomes smaller, and hence the emittance. The so-called normalized emittance

Considers these Emittanzverkleinerung and - if the particle acceleration is the only nonlinear effect is - a conserved quantity. ( Since all charged particles emit synchrotron radiation, the normalized emittance, however, is only a good approximation, a conserved quantity. )

For light charged particle ( such as the electron ) is confronted by the synchrotron radiation damping a Emittanzgleichgewicht a ( equilibrium emittance ).

There are various definitions of emittance, since the edge of the area is not well defined:

• 95 % - and 90% - emittance: 95 % (90 % ) of the particles are within the phase space volume;
• RMS emittance: based on the standard deviation;
• Convention: π is usually counted to unity, it means the unit eg π · mm · mrad.

For free-electron laser is the so-called " Slice emittance " an important variable: Instead of a beam, bunches, called Bunche located in the accelerator. These packages can be cut into smaller slices, and assign each of these discs a emittance. This is the so-called slice emittance, which is important especially for the lasing of the FEL.

The emittance is an important physical quantity in accelerator physics, where it usually it arrives in large particle accelerators to achieve the smallest possible beam emittance, ie, to produce a highly focused beam of particles has a small cross -sectional area, the particle on its way in a particle also to stay focused (ie not " " smeared "or diverges ). A related term used in light optics is the brilliance.