The apparatus is shown schematically in figure 3.6, in the
configuration used to make TOF measurements. Its main
features are described in detail in chapter 2. In order to measure electron flight-times, a beam tagger prior to the scattering cell was employed and a flight tube and repeller grid were incorporated after the s c attering cell. The retarding field profiles were measured, w i t h the tagger removed from the beam-line, using an analyzer grid in front of the electron detector (Cl).
A primary positron beam was obtained by the m o d e r a t i o n of (3'^ particles emitted by radioactive p o s i t r o n sources, using W meshes. The TOF m e a s urements were m a d e with a 4mCi ^^Na source resulting in a primary beam w ith an intensity of around 4xl0^s'^. The beam was accelerated to a m e a n energy of around 3 50eV before being guided to a second m o d e r a t o r (M2), incorporated in the beam tagger. The o p eration of this device is described in section 3.3. The retarding field m e a s u rements were made w ith a beam w i t h an intensity of around IxlO'^s'^ derived from a 70mCi ^Na source. The beam was in this case transported to the interaction region w i t h the tagger retracted from the beam-line.
The interaction region comprised the gas s c a ttering cell and ion extractor d e scribed in section 2.4. Following positron impact ionisation of gas atoms, electrons ejected in the forward direction were transported along a flight-tube of around Im in length by a u n i f o r m m agnetic field set up inside a solenoid. The electrons w e r e d etected at the end of the beam-line using Cl, as shown in figure 3.6.
A repeller grid, between two earth grids a p p r o x imately 9mm apart, was placed just after the exit aperture of the scattering cell. A potential of around 500V was applied to this grid in order to prev e n t positrons from t r a velling further along the beam- l i n e and liberating secondary
electrons from grids near the electron detector. Cl,
Ceratron Source and Moderator Assembly Two Element Cylindrical Electrostatic Lens Electrode Array Etched on P C B M2 Repeller Grid Analyzer Grid CEMA
Primary Positron Beam
Ejected Electrons 7777 Hemispherical Scattering Cell 7777 7777 Beam Tagger Assembly
Guiding Magnetic Field
CD
03
spectra. The use of this grid did however cause positrons to be reflected back through the interaction region. The effects of m ultiple traversals are d i scussed below.
The magnetic field strength from the scattering cell onwards was reduced to around lOG, in order to reduce the pitch angles of the incident positrons and to limit the angular acceptance of the electron d e t e c t i o n system, so that only those electrons ejected at small angles, relative to the beam axis, would be confined by the m a g n e t i c field to reach Cl. By limiting the detection system to accept only those electrons with small transverse components of kinetic energy, the measured longitudinal component was appr o x i m a t e l y equal to the total kinetic energy. Additionally, according to certain theories, the ECC electrons w ere expected to be ejected at small angles in the forward direction.
3.2.1 The Transmission Probability Function
In order to estimate the angular acceptance of the electron detection system, the tran s m i s s i o n prob a b i l i t y function, T{E,6), of the apparatus was estimated. T(E,0) is defined as the probability of an ejected electron p a s sing through the exit aperture of the scattering cell and reaching the active area of the detector, as a function of emission energy (E) and angle (6), relative to the incident beam. T(E,#) was estimated by solving the equations of m o t i o n for electrons with a given E and 6 but w i t h a large number of different starting co-ordinates, equally spaced over the entire range of possible starting points w i t h i n the interaction region. The ratio between the total n u mber of trajectories and the number of trajectories passing thro u g h the exit aperture of the scattering cell and r eaching the d etector was then used as an estimate of the trans m i s s i o n probability.
Throughout this derivation, the m a g n e t i c field strength is assumed to be uniform and not time varying. In vector notation, the equation of m o t i o n of a charged part i c l e with
velocity y, in a magnetic field B may be written
- ^ = - 2 (v xB) (3.2)
at m
where q and m are the charge and mass of the particle respectively. If a cartesian co-ordinate system is chosen so that the z-axis is parallel to B, e quation (3.2) may be r e written
where
f (3.4)
and Vx and Vy are the components of v e l o c i t y in the directions