The high sensitivity of the KATRIN experiments will be reached by a special type of spectrometers, so-called MAC-E-Filters (Magnetic Adiabatic Collimation combined with an Electrostatic Filter). This type of spectrometer was first proposed in [1] and described in [2][3]. It combines high luminosity and low background with a high energy resolution, both essential to measure the neutrino mass from the endpoint region of a beta decay spectrum.

The main features of the MAC-E-Filter are illustrated here. Two superconducting solenoids are producing a magnetic guiding field B. The beta electrons, which are starting from the tritium source in the left solenoid into the forward hemisphere, are guided magnetically on a cyclotron motion around the magnetic field lines into the spectrometer, thus resulting in an accepted solid angle of up to 2 .

On their way into the center of the spectrometer the magnetic field B drops by many orders of magnitude. Therefore, the magnetic gradient force transforms most of the cyclotron energy into longitudinal motion. The animation on the right illustrates this by a momentum vector. Due to the slowly varying magnetic field B the momentum transforms adiabatically, therefore the magnetic moment µ keeps constant (equation given in non-relativistic approximation):

This transformation can be summarized as follows: The beta electrons, isotropically emitted at the source, are transformed into a broad beam of electrons flying almost parallel to the magnetic field lines. This parallel beam of electrons is running against an electrostatic potential formed by a system of cylindrical electrodes. All electrons with enough energy to pass the electrostatic barrier are reaccelerated and collimated onto a detector, all others are reflected. Therefore the spectrometer acts as an integrating high-energy pass filter. The relative sharpness of this filter is given by the ratio of the minimum magnetic field B_min in the center plane and the maximum magnetic field B_max between beta electron source and spectrometer :

                  

Varying the electrostatic retarding potential allows to measure the beta spectrum in an integrating mode.
 

[1]   G. Beamson et al. , J. Phys. Sci. Instrum. Vol. 13 (1980) 64

[2]   V.M. Lobashev, Nucl. Inst. and Meth. A240 (1985) 305

[3]   A. Picard et al., Nucl. Inst. Meth. B63 (1992) 345