16.1 Plasma instrument: The top-hat
The top-hat electrostatic analyzer is a well known type of ion deflector and has been introduced by
Carlson et al. (1982). It can be schematically represented by two concentric hemispheres, set to opposite
voltages, with the outer one having a circular aperture centered around the symmetry axis (see Figure 104).
This entrance allows charged particles to penetrate the analyzer for being detected at the base of the
electrostatic plates by the anodes, which are connected to an electronic chain. To amplify the
signal, between the base of the plates and the anodes are located the MicroChannelPlates (not
shown in this picture). The MCP is made of a huge amount of tiny tubes, one close to the next
one, able to amplify by a factor up to the electric charge of the incoming particle. The
electron avalanche that follows hits the underlying anode connected to the electronic chain.
The anode is divided in a certain number of angular sectors depending on the desired angular
The electric field generated between the two plates when an electric potential difference is
applied to them, is simply obtained applying the Gauss theorem and integrating between the internal
() and external () radii of the analyzer
||Outline of a top-hat plasma analyzer.
In order to have the particle to complete the whole trajectory between the two plates and
hit the detector located at the bottom of the analyzer, its centripetal force must be equal to
the electric force acting on the charge. From this simple consideration we easily obtain the
following relation between the kinetic energy of the particle and the electric field :
Replacing with its expression from Equation (97) and differentiating, we get the energy
resolution of the analyzer
where is the distance between the two plates. Thus, depends only on the geometry of the
analyzer. However, the field of view of this type of instrument is limited essentially to two dimensions since
is usually rather small (). However, on a spinning s/c, a full coverage of the entire
solid angle is obtained by mounting the deflector on the s/c, keeping its symmetry axis
perpendicular to the s/c spin axis. In such a way the entire solid angle is covered during half period of
Such an energy filter would be able to discriminate particles within a narrow energy interval
and coming from a small element of the solid angle. Given a certain energy
resolution, the 3D particle velocity distribution function would be built sampling the whole solid angle
, within the energy interval to be studied.