Noise

The noise associated with the spatial mapping of the beam can be traced back to 5 main contributions:

• Ion drift: systematic contribution coming from the drift of the created ions in the extraction field. Simulations performed on the model introduced in section 6.1.5, presented later in this section, predict this contribution to smear each point in the image according to a Gaussian distribution with standard deviation of 0.93 mm in any direction.

• MCP spatial resolution: introduces a smear of each point whose size is given by the pitch between different channels (12µm), plus the spread affecting the elec- trons from each separate channel as they travel between the two MCPs forming the chevron configuration and towards the phosphor screen. The manufacturer quotes a spatial resolution of 80µmfor the particular detector used in this work. This contribution needs to be added in a quadratic sum to the smear due to ion drift, and can be therefore considered negligible.

• Residual gas pressure fluctuations: instabilities or inhomogeneities in the residual gas pressure leads to distortion or oscillation of the imaged profile. The effects of this contribution have been tested (see later in this section), but prove negligible when compared to the ion drift contribution.

• Electric field stability: the stability of the electric field affects both the electron beam and the extracted ions, and also includes the contribution of the stability of the electron gun power supply, controlling the electron beam energy and intensity. The effects of this contribution have been tested (see later in this section), and can be important when occasional strong spikes occur and the extraction field voltage changes abruptly in intensity. However these are isolated events occurring with

a frequency of few events per hour and lasting about 100-500 ms, and are not detectable during normal operation of the monitor. The most likely cause of these events has been identified in a fault of the communication protocol of the power supply to the computer. Indeed, direct connection with the computer, rather than through the use of a hub, reduces the frequency to about 1 event per hour.

• Spontaneous residual gas ionizations: it is in principle possible for the resid- ual gas to self ionize, e.g. following a collision with other residual gas molecules, and hence produce a signal on the detector. To isolate this effect measurement were taken with the electron gun switched off. However, no detectable signal was visible in the pressure range of 5·10−9÷10−6 mbar: it is concluded that spon- taneous residual gas ionizations have a negligible impact on the measurement.

Ion drift and MCP spatial resolution The contributions of ion drift and MCP spatial resolution are intermingled in the measurements, as they have similar effects; however they behave differently with respect to the extraction voltage: increasing the extraction voltage decreases the spread due to ion drift but does not affect the MCP contribution.

With reference to eqn. (7.2), the combined contribution of the two effects can be evaluated from Fig. 7.4, by considering the intercepts of the three curves. The theory presented in section 6.1.5, modeling the extraction with a homogeneous field and the initial velocity distributions with components coming from recoil and thermal motion, can be used to provide a theoretical prediction for the quantities given in table 7.2. The same simulation leading to Fig. 6.6 is run for a 12 kV/m extraction field, assuming gas at room temperature and collectively at rest (as opposed to the jet which has a collective velocity in thex direction); and all ionizations to come from a single point in space (hence omitting the effect of finite gas screen width). For an extraction field of 12 kV/m, the simulation yields the plot shown in Fig. 7.5: the probability distribution for the location of the imaged point resulting from an ionization in the extraction field center.

As compared to Fig. 6.6, Fig. 7.5 shows a more symmetric shape, explained by the absence of the spread due to the gas screen width. The standard deviations of both profiles is equal since strongly dominated by the initial velocity component due to gas temperature, which is isotropic. In particular,σresgasproves to be almost 6 times larger

7.3 Performance characterization

Figure 7.5: Probability distribution function of a particle from the residual gas ionized inx= y = 0 to be imaged in the pointx z; equivalent to the 2-dimensional spot resulting from ionizations in x = y = 0. 1-dimensional profiles also shown. This image is the residual gas equivalent of Fig. 6.6, which is instead calculated with the parameters of a gas-jet target. The much increased spot size is due to the much higher temperature of the residual gas as compared to the gas jet. This simulation uses the approximation of ideal field and projectile trajectories. Statistical ripple due to low number of counts is observed at the tail of the distributions, in particular along the y axis. The parameters used are a homogeneous electric field of 12 kV/m and a temperature of 300 K. For both 1-dimensional profilesσ = 0.93 mm.

than σz of the jet, and more than an order of magnitude larger than σx of the jet as

presented in table 6.1. This is due to the low temperatures achieved during the gas jet expansion, and illustrates another advantage of supersonic gas jet profile monitoring over residual gas profile monitoring.

The same simulation leading to Fig. 7.5 is repeated for 20 and 30 kV/m extraction fields, yielding standard deviations for the 1-dimensional density distributions of 0.67 and 0.55 mm respectively, in agreement with the experimental results (c.f. table 7.2). These values of standard deviation confirm the contribution due to MCP channels pitch to be negligible compared to the ion drift due to thermal velocity in a room temperature residual gas.

Another feature of interest in assessing the errors affecting the measurement of the beam profile is the homogeneity of the error due to ion drift contribution across the observation region. Indeed, any inhomogeneity would cause the image being spread more in some places than in others, resulting in profile distortion. To assess this effect the electron beam was scanned across the observation region, and transverse beam profiles traced for several points at different x coordinates. For these measurements, the electron beam was focused at the size of 2 mm FWHM, measured at the center of the observation region on the retractable phosphor screen, so as to make the effect of variation inσdrif t most apparent. The results of the experiment are shown in Fig. 7.6.

The points in Fig. 7.6 show a relatively large spread of about 10%. However, translated in pixels, the spread goes from 30 to 33 pixels, and is hence comparable with the resolution error of the monitor of ±1 pixel. It is concluded that no significant variation in beam size is observed across the monitor field of view.

Medium term stability test A test of the medium term stability of the measure- ment, intended to evaluate the residual gas pressure and electric field stability, has been performed by recording a video file from the CCD camera and analyzing the image over an observation time of 10 minutes. The same test was repeated 20 times in different days, and the results added together for a total of 200 minutes observation time. During the observation time the monitoring parameters of bias voltages was kept constant and residual gas pressure and focus of the electron gun, coarsely fixed by the position of the control knobs were finely adjusted at each new measurement to match the observation

7.3 Performance characterization

Figure 7.6: FWHM of the beam measured in different points across the observation region.

of the first day. This was made necessary due to an insufficient accuracy of the electron gun focus control and the hot cathode pressure gauge.

An indication that this procedure was needed was given by the fact that in a first set of measurements, in which this calibration was not done, the measured stability on the 10 minutes observation time, in each time window, was consistently better than the stability of the sum of all windows. Also, the percentage oscillation in each 10 minutes window was comparable (3÷4%), and better than the overall stability, which was measured up to 19%. Therefore it is concluded that the discrepancy between different observation windows comes from wrong initial setting, given by inaccurate control of the electron gun focus and pressure gauge.

The signal profile was sampled every 10 seconds. The standard deviation of the distribution of oscillation amplitudes between corresponding points was measured to be 4.1% in the tail regions, where the signal is weaker, due to the higher impact of the noise. In the central region, where the signal is larger than half its maximum value, the oscillation amplitude is reduced to 1.6%.