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 $6 10$ 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 resolution.

Figure 104:

Outline of a top-hat plasma analyzer.

The electric field $E(r)$ generated between the two plates when an electric potential difference $dV$ is applied to them, is simply obtained applying the Gauss theorem and integrating between the internal ( $R1$ ) and external ( $R2$ ) radii of the analyzer

In order to have the particle $q$ 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 $E k$ and the electric field $E(r)$ :

Replacing $E(r)$ with its expression from Equation (97 ) and differentiating, we get the energy resolution of the analyzer

where $dr$ is the distance between the two plates. Thus, $dEk/Ek$ 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 $dY$ is usually rather small ( $~ 5o$ ). However, on a spinning s/c, a full coverage of the entire solid angle $4p$ 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 spin.

Such an energy filter would be able to discriminate particles within a narrow energy interval $(E ,E + dE ) k k k$ and coming from a small element $d_O_$ of the solid angle. Given a certain energy resolution, the 3D particle velocity distribution function would be built sampling the whole solid angle $4p$ , within the energy interval to be studied.