Investigation of Beam Performance Parameters in a Pierce-Type Electron Gun

In the present work, an investigation has been made for the ext raction characteristics and beam diagnosis for a Pierce-type electron gun with spherical anode to acquire an electron beam suitable for different applications. The acceleration voltage increases the electron beam currents up to 250 mA at Accelerat ion voltage 75kV and decreases the beam perveance, beam waist and beam emittance. The min imum beam radius could be found at the min imum beam perveance and maximum convergence angle. Also the increase of the accelerating voltage affects the increase of the beam fluence rate up to 1.3 x 10 e/min.cm, due to the increase of the extracted current. Tracing the electron beam profile by X-Y probe scanner along the beam line at two different places reveals that the spherical anode affects the beam to be convergent. The electron beam could be suited for the two suggested experiments in our lab, p lasma acceleration and surface modifications of polymers.


Introduction
The development of electron beam devices has a long history and electron beam technology has undergone several changes over the years. A variety of electron beam sources have been designed and utilized in the basic research as well as for the industrial applications [1][2][3]. The electron beam parameters such as diameter, current, energy, etc. were adjusted to suit their specific experimental requirements [4]. Charged particle beams fro m different types of sources have to be transmitted without loss of the particles through the accelerator. It is very important that the particles strike the target should have the parameters required for a certain application. For a beam transmission without loss of the particles, the cross-section of the beam must not exceed a given maximu m value of a well-defined point. To achieve this we will introduce an important quantity known as emittance wh ich one wants to min imize for any given current [5]. The emittance is an important aspect for high-quality beam, which is basically defined by the product of the width and transverse velocity spread of the beam (region of phase space occupied by beam). If the beam is densely packed, then the emittance is said to low. Whereas beam that is somewhat spread out has high emittance [6][7][8].
Knowing the beam propert ies before its in jection into the accelerator saves the time needed for accelerator tuning and

Experimental Setup
The electron beam is produced fro m a Pierce-type electron gun (figure 1) with an indirectly heated cathode operating in a diode circu it. The Pierce electrode makes an angle 67.5 o with the beam edge. The cathode, together with the beam shaping electrode, is connected to a pulse modulator which provides negative high voltage (up to 80 kV) pulses with variable pu lse repetition rates (fro m 31.25 to 500 counts/s) which accelerates the electrons with a velocity of about 0.5c (the velocity of light). The anode with a spherical shape is grounded to the vacuum chamber i.e. considered positive with respect to the cathode and the beam shaping electrodes. In the field free reg ion behind the anode, a chamber exists having three flanges, figure 1. The gun section is connected to the field free space chamber through an aperture in the anode electrode. The electron beam scanner, shown in figure 2, is an electro mechanical system with a thin long wire (0.1mm d iameter and 100mm long) is used for probing the beam to study the dependence of beam parameters on the acceleration voltages.  The scanning probe moves in the direction of the beam (z-direction) and moves in a direction perpendicular to the beam d irection. The scanning probe is placed at distances 20mm (at the beam waist) fro m the anode, and a set of currents I p values is recorded for different Acceleration Vo ltages. Then the probe is shifted to a new distance 150mm (at the beam exit) fro m the anode, and the previous procedures are repeated. More details about this scanner could be found in literature [10]. Figure 3 shows the influence of the Acceleration voltages on the ext racted electron beam current and perveance. The electron beam current increases (fro m 20mA up to 250mA ) with the increase of the Acceleration voltage up to 75kV, this dependency is in close agreement with child-Lang muir [11]: 6 3/ 2 7.31 10

Studying Electron Beam Intensity and Perveance
Where, r a is the beam radius at the anode exit aperture and d is the distance between the cathode and the anode.
At higher acceleration voltages, the increase of the electron beam current is limited and the current seems to be quasi-saturated in this reg ion. Th is quasi-saturation effect is due to the fact that, the nu mber of the backscattered electrons increases with increasing the electron energy [12,13]. Space charge effect in beams is conveniently characterized by the perveance taking into account the magnitude of the beam current and the acceleration voltage [14]. Figure 1 shows that the perveance decreases with the increase of the accelerat ion voltage. The beam perveance decreases from 5.7 x 10 -2 µperv down to 1.2 x 10 -2 µperv and the Acceleration voltages increase from 5kV up to 75kV respectively. For values of the perveance P ≤ 10 -2 µperv the intrinsic electric field of the beam has an appreciable effect on the motions of the electrons. But for values of P ≥ 10 4 µperv, the effect of space charge can be neglected [15].

Electron Beam Profile and Emi ttance Analysis
Here we will trace the beam profile which describes the current intensity distribution, the beam width, and the angular divergence of the beam. For plas ma acceleration experiment, the in jected electron beam has to be very thin, with h igh convergence angle and very low emittance. These conditions are achieved at the electron beam waist which is located at a distance 20 mm fro m the anode aperture. So that, the electron beam profile is traced at th is point to find the optimu m conditions for performing the plasma acceleration experiments. The traced profile (at accelerat ion voltages 36kV, 48kV, 60kV and 75kV) is shown in figure 4a which is fitted to the Gaussian function, and the fitting parameters are shown in table 1. The produced beam has to be wide to match the experiment of electron beam treat ments of materials for surface modification. The electron beam is found to be wider and the convergence angle is larger and hence the beam emittance is larger at the Faraday Cup (FC) i.e. target holder. So that the beam profile is traced at distance 150mm fro m the anode aperture as shown in figure 4b. This figure shows two peaks which are fitted Gaussian and shown in figure 5. The deduced fitting data are also summarized in table 1. Table 1 shows the variations of the beam parameters with different beam energies. In such a table we can see the parameters; x c is the centre of the beam, w is the beam fu ll width at half maximu m (FWHM) and A is the area under the curve. Table 1 shows that;1) the beam width decreases with energy i.e. raising beam energy focuses the beam.2) Electron beam current intensity increases with the beam energy; this is proved by the increasing of A and the increasey c (the beam height).
3) The beam centre changes and deviates from zero point; this may be due to the strong repulsive force which increases as the electrons become closer to each other i.e. the beam is focused [16].  Increasing the acceleration voltages, increases the axial component of the accelerating field with respect to the transverse component which affects the beam to spread and thus allowing the beam to become more convergent [17]. The velocities of the electrons emitted perpendicular to the cathode surface have two co mponents; axial and transverse. Therefore, the angle of beam divergence γ is found to be in the form [20]; kT eU γ = (4) Since eU is the axial accelerat ing energy of the electron beam. Fro m such an equation, it is seen that γ is proportional to the electron temperature and inversely proportional to the accelerating voltage U, i.e. the increase of the anode voltage causes a decrease of the beam width and emittance. As the electrons approach the axis of the beam, the colu mb ic repulsive force increases, this effect leads to the escape of electrons towards the beam boundaries. This phenomenon explains the splitting of the beam profile curves shown in figure 4b. Under the action of the anode lens these two peaks disappear, figure 4a. After the beam escapes from the anode lens field, the beam splitting appears, figure 4b. Figure 6 shows the variation of the beam rad ius at waist and at the FC entrance with the variation of the electron beam perveance. The electron beam radius increases with the increase of the electron beam perveance. Hence to obtain a minimu m beam waist we have to use a low perveance beam. These results are in a very close agreement with the computer simulat ion results previously reported [21].Finally, the increase of the beam width with the increase of z and the decrease of this width with the increasing of the ext racting voltages are ev ident fro m figures 4 and 5. The space charge effect is believed to be the cause of the divergence of the electron beam; while the focusing property of the anode aperture imp roves the beam profile confinement i.e. focuses the electron beam.
The emittance is being roughly proportional to the ratio of transverse velocity to axial velocity of the electron. This rat io gives the slope of the trajectory leaving the emitting surface. If the emitt ing surface is a circle with radius r c , then the normalized emittance is defined as [19]: And the transverse emittance is given by: The envelope of is an upright ellipse with extreme values ( ); then its area is , so: For small values of , Where; r is the beam radius and z is the distance from the exit aperture of the beam to the scanning probe. The increase of the acceleration voltage decreases the width and the divergence angle of the electron beam and hence the electron beam emittance decreases. Table (2) confirms the princip le which states that themin imu m beam rad ius is found at minimu m beam perveance and higher beam convergence.

Electron Beam Fl uence Calcul ati on
Electron beam absorbed dose is used to identify the electron beam radiation in the science of dosimetry. Also the following quantities are used to describe an ion izing radiation beam (electron beam): part icle fluence, energy fluence, particle fluence rate and energy fluence rate. These quantities are usually used to describe charged particle beam [22,23]. In this work we will use the terms, electron beam fluence and fluence rate to describe the electron beam in the irradiat ion of materials surfaces experiments. According to the definitions of fluence and fluence rate, , , r γ ε these parameters are calculated and shown in figures 7 and 8.
The particle fluence φ (measured in m -2 ) is defined as the number of particles dN incident on cross-sectional area dAand could be expressed as in the formula; φ = dN/dA, While the particle fluence rate φ′ (measured in m -2 s -1 ) is the increment of the fluence d φ in time interval dt and could be expressed as φ′= d φ/dt. Figure 7 shows the increase of the fluence rate (number of electrons incident on a specific area per second) with the increase of the acceleration voltage. The ma ximu m number of electrons enter the FC are 1.56 X 10 18 electrons at acceleration voltage 75 kV. The fluence rate is in the range fro m (2 x 10 16 up to 2.21 x 10 17 ) electrons/s.cm 2 at energies between 5keV and 75keV respectively.According to the irradiation t ime the electron beam fluence is calibrated at electron beam energy 75keV. Figure 8 shows a straight line, its slope (1.3 x 10 18 e/min.c m 2 ) represents the electron beam fluence rate.

Conclusions
Different types of electron guns have been designed for producing different electron beam energies. In this work, a Pierce-type electron gun with spherical anode has been investigated to produce an electron beam with suitable properties valid for the suggested application in our laboratory.
Upon investigation of the designed gun, it has been found that the acceleration voltage increases the electron beam currents up to 250mA and decreases the beam perveance. The spherical ext raction electrode (anode) is believed to produce a convergent beam. This effect is proved by tracing the electron beam density distribution at two different places along the beam line. Also it is found that the distribution of the electron beam affected by the accelerat ion voltage i.e. the electron beam d iameter increases with the decrease of the acceleration voltage. So that the higher the acceleration voltage, the lower the beam emittance.
Electron beam emittance is preferably to be as low as possible for the suggested plasma acceleration experiment. While the polymer t reatment experiment requires a spread out beam with larger d iameter i.e. with high emittance. It is proven that the min imu m beam radius could be found at the minimu m beam perveance and maximu m convergence angle.
Also the electron beam fluence rate and electron fluence are considered and calcu lated, these two values depend on the acceleration voltage. We can conclude that the resulting electron beam (density and shape) could be controlled by not only the gun geometry but also the acceleration voltages to produce a suitable electron beam for different applications.