Cerenkov Radiation

Apparatus

The experimental setup is fairly straightforward: Three power supplies (one just used as a ground) are connected to the electron gun, one of which is regulated by a control box. The gun, the dielectric, the phosphor screen, the deflection plate and the diode are all placed in a vacuum chamber that is pumped to ~10-6 Torr. The diode voltage (hypothetically) changes in the presence the radiation, a change reported by the multimeter to the computer. A GUI written in LabWindows (see Appendix G) allows the user to see a plot of the incoming data in real time. The data (diode voltage, deflection voltage, and time) is then saved to several *.xls (Excel format) files for later use. Beam deflection was controlled in the GUI since the deflector’s power supply could be connected to the computer. Despite its simplicity, the system was plagued by problems. The two high voltage power supplies were designed with 3 KV at the top of their operating ranges, and as such they did not operate optimally. Neither was the current control box for the gun designed to be operated at these voltages and was plagued by arcing throughout the experiment. The gun itself was not immune to failure either. Several shorts developed along the body of the gun, leading to numerous rebuilds (and since once a filament has been used it is very brittle and prone to breaking, this also led to several filaments being replaced).

Electron Gun

The electron gun used was a custom built , cylindrical electrode gun, built by a previous MXP project (Kopp and Fishpaw). At the outset of the project, gun was rebuilt to ensure functionality and quality (as the gun had been damaged somewhat since its last use). Then the beam characteristics were explored through the use of a phosphor screen placed down stream from the gun.

Design

The design consists of three stainless steel cylinders set at different voltages, each modulated to control the energy and focus of the beam. There are also several focusing electrodes (plates with small circles milled in them, used to focus the beam). A tungsten filament in the first cylinder is heated to generate the electrons for the beam. The remaining cylinders accelerate the electrons and focus them into the beam for the experiment. The entire assembly is mounted to a four-port BNC vacuum plate and extends approximately 17 cm into the chamber. The cylinders and electrodes are in turn mounted to four alumina rods. Several plates are positioned at various points in the structure to ensure the alignment of the cylinders.

The first cylinder’s voltage (V1), and indeed the filament’s too, is controlled by a circuit shown in Fig. 8. A Variac is used to control the current across the filament.

The control box for the filament (and V1) was built by Dwinnel and Reuteler for a previous MXP project. For the initial beam calibration tests a NerdOTronix negative high voltage supply powered the control box. A Hewlett-Packard Harrison DC power supply gave the V2 voltage, while the V3 was powered by a Heathkit Regulated high voltage power supply. For the primary data runs, the HP supply was used for V1 and a Power Designs high voltage calibrated DC power source was used for V2.

Several times during the project, the gun was adjusted to eliminate shorts, arcs, and other troublesome behavior. During these repairs the filament often broke (the filament becomes very brittle after being used in the vacuum, and thus prone to breaking) and had to be replaced. See Appendix A for more information about the electron gun.

Calibration

To experimentally determine the optimal relationship between voltage settings, and to explore the beam properties at various distances from the gun, a phosphor screen was placed in the beam’s path within the chamber. A cable ran along the exterior of the chamber from the screen’s external connector to the exterior of the V1 voltage line into the gun, thereby grounding the screen and keeping it from building up any net charge.

By observing the beam diameter as a function of V2 (voltage on the middle cylinder) and V3-V1 (the combined voltage difference of the gun), the following relationship was determined

This is a fine first order approximation, but there is also pronounced second order effect, one which was characterized more effectively with the use of the SIMION program.

SIMION

This program made it possible to model the behavior of the electron gun and to visualize the effects of different voltages on the performance of the gun. The first step in utilizing the software was to “build” the gun in the program. See Appendix B for some of the visualizations generated by the program as well as a brief discussion of problems encountered while using the program.

Vacuum System

The vacuum chamber itself consists of a large stainless steel sphere with six large openings in cubic symmetry. The bottom opening is fixed the pump system. There are also 4 smaller openings at the corners. For the beam calibration tests, the phosphor screen was placed in the opening opposite the gun, with the two pressure sensors placed in the remaining two small openings. Glass view ports were placed in the lower and right-handed larger openings, with the remaining three ports (upper, left and the top of the chamber) were covered.

Since we need an ultra-low vacuum (10^-6 Torr, ten order of magnitude below standard room pressure), two pumps and two pressure gauges are needed. The first stage is a vane pump capable of quickly achieving pressures of 10-1 Torr. A Pirani gauge is used to monitor the pressure from standard to about 10^-2 Torr. At 10^-1 Torr, the second pump, a turbo pump , is activated. This stage can quickly achieve a pressure of 10^-6 Torr. For these pressures, the Pirani gauge is no longer accurate, so we switch to an ion gauge . See Appendix C for more information.

Experimental Design

In order to generate microwave Cerenkov radiation, the electron beam must be both well defined and accurately positioned. The beam must pass within a millimeter of the dielectric surface, and it must travel in a manner which is parallel to the plate.

Dielectric Positioning

The dielectric chosen for this project is titanium dioxide ceramic (dielectric constant of 80-100). Polycrystalline titanium dioxide had been used in the first observation of microwave Cerenkov radiation by Danos, et al in 1953. The piece used in this experiment is 25 cm square by 0.5 mm. It was suspended beside the path of the electron beam on a custom mount (similar to the construction of the electron gun).

Titanium dioxide (in its pure form) comes in two distinct structural forms (as seen below). The larger form (on top) is referred to as anatase, while the smaller form is called rutile [16]

Beam Deflection

The electron beam that comes out of the gun is aimed slightly to the right. To correct for this deviation, a steel plate was installed parallel to the dielectric. This plate was in turn connected to a DC power supply that could be controlled by the computer (via GPIB). A simple program in LabWindows allows the user to generate a square wave function of a specific VPP, frequency and DC offset. This was used to generate a pulsed electron beam. At low frequency (compared to the frequency of the radiation) pulsed beam also gives a pulsed radiation signal, thus making it easier to extract the signal from noise in the frequency domain.

Some trials were conducted in SIMION to see if plates as small as that being considered could indeed deflect the beam enough. Based on these constraints, the plate would have to be brought to a few hundred volts to work.

Having the deflection plate gives the user far greater control over the proximity of the beam to the dielectric. With appropriate tuning, a square wave sent to the plate could put the beam very close to the dielectric at the bottom of the signal and then pull the beam more than an inch away from the dielectric at the top of the signal, thus eliminating the possibility of generating any radiation. This deflection system was built and installed, but was not utilized due to difficulties in programming the associated power supply.

According to an earlier plan (set forth in the spring), one using two sets of plates placed just beyond the electron gun, one could both measure the energy of the electron beam, control its positioning, and "chop" it. While parts of this earlier system were built, this addition to the system was not completed in time for experimental trials. The theory for the dual deflector, however, was worked out.

We know the energy of an electron beam moving in the x direction can be measured by passing the electron beam between two plates with a voltage difference between them. We consider only particles in which

This makes the calculations easier, since the particle’s behavior can be approximated as non-relativistic. An individual electron experiences a force of

when it is in an electric field. The electron would therefore experience a change in momentum of

In this case the electric field is perpendicular to the path of the electron; therefore, the change in momentum is solely in the y direction. The electric field between the plates is

The time the electron passes between the plates is the same no matter how large E is since the velocity in the x direction remains constant. Thus, the time the electron spends between the plates is

and the momentum of the electron in the y direction after it passes through the plates is

By measuring the distance the particle travels in the x and y direction we can find

since,

and therefore,

For more information, see Appendix D

Sensors

To detect the microwave radiation expected from the setup described above, a microwave diode was used. The diode used is sensitive to X-band microwaves of a certain linear polarization. This band covers frequencies from 8 to 12 GHz (3.75 to 2.4 cm). A separate series of tests with a microwave transmitter of known parameters showed the diode was in fine working order at atmospheric pressure, yielding over 30 mV when aligned correctly with the transmitter. When rotated by 90°, the signal vanishes, as expected.

When the diode was initially placed in the vacuum chamber the noise level was very small (on the order of hundreds of micro-volts). When the pumps were turned on, however, there was a severe increase in the signal. A similar phenomenon was observed during the rapid restoration of pressure at the end of each session; in this scenario the voltage drops dramatically (even going negative). In both cases the voltage slowly travels back towards the background levels.

This sloping is not asymptotic to this level, however, but rather the voltage seems to oscillate about the background (as a heavily damped harmonic oscillator).

Several trials were conducted with the microwave transmitter to determine if this unexpected behavior in any way affected the responsiveness of the diode. For these tests, the diode was placed in the chamber with the dielectric. The microwave source was placed approximately 40 cm from one of the windows on the chamber (approximately 65 cm from the diode itself, with the diode rotated 45° from the path of the microwaves). First the responsiveness of the diode in the chamber at air pressure was tested. For these tests, an external microwave source was used (see picture below).

The increase in diode voltage resulting from being exposed to the microwave source was clear and sharp, with the voltage dropping back to background levels within 0.5 seconds. Then the diode was tested during the pumping sequence and at 10-5 Torr (the pressure at which the gun trials would be conducted). Here too, the diode voltage responded clearly and appropriately.

During the gradual curve in diode voltage immediately following the activation of the vane pump the behavior of the diode voltage while the microwave source was on seemed to show that it was sloping back to the levels set by the microwave source before pumping. This accounts for the difference in voltage increase (increase between background voltages and those when the microwave source is on) between the air pressure and low-pressure tests. The final piece was to test the diode’s response to the activation and modulation of the electron beam. While at low pressure, the gun was activated and the beam was brought to ~2900 V (Variac up to 70%), with no discernable change in diode voltage. A magnet was used to move the beam back and forth, still with no change in diode signal.

After these tests, it was determined that the diode’s behavior during pumping, while unexplained, did not hamper the responsiveness of the diode to an outside microwave source. Given the large response of the diode to the 8mW source used in the trials, one is encouraged that the diode may visibly show the much weaker Cerenkov signal (estimated to be less than the 10-6 W expected by Danos).

For data collection, the diode signal was passed to an HP multimeter that was, in turn, connected via a GPIB cable to a computer for further analysis. This system has a maximum sampling rate of 2 Hz and a measurement precision of ±10 nV.