The initial plan was to explore the threshold conditions for Cerenkov radiation as well as the angular and wavelength distributions. Due to the instability of the system only one set of good, clean data could be taken in the spring. In the summer the entire experiment was disassembled and rebuilt. Following this, the system was far more stable, and several sets of data were collected. Below is the original data and analysis from the spring. Following that is the summer data and its analysis

The data that will be subsequently analyzed was collected with the diode positioned directly behind and in close proximity to the dielectric in order to receive a maximum percentage of the radiation.

Spring Data

During the trial, the gun only operated without incident for approximately 1200 seconds. During this time, 400 seconds of clean data was taken. Afterwards, arcing caused a clear and noticeable shift in the data, making all subsequent data suspect. The 400 good data points were collected approximately three hours after turning on the pumps. By this time, the diode had settled at a nearly constant value. For the first 100 seconds of this data, the gun was set to a net potential difference (V3-V1) of 3 KV, with V2 set to –2360 V for focusing (the Variac was set to 70, while V3 was set at ground). At these settings, the beam had an approximate diameter of 4.5 ± 0.5 mm and was positioned 1.3 ± 0.5 mm from the dielectric surface. Using equation 39 one finds that the radiation (again, if any was generated) would have its greatest intensity at wavelength (assuming )

Of course this is to the center of the beam, the beam was actually grazing the surface of the dielectric. If one wants to observe X-band Cerenkov radiation, the distance needed is

During the subsequent 100 seconds, V1 was turned down to 2990 V (below the threshold for Cerenkov radiation). The cycle of above threshold for 100 s, then below for 100 was repeated once more (actually it was repeated three times more, but arcing ruined the accuracy of those measurements). Shortly after this data was taken, the V1 power supply began to behave very erratically, and the trial was terminated.

The figure above shows the plot of the voltage vs. time data (straight from the diode) for all 400 seconds to be analyzed. Notice that the resolution of the multimeter is a significant problem here.

Graph 2 shows the voltage across the microwave diode as a function of time. The electron gun had remained off the entire time, the vacuum chamber started at air pressure and then was pumped down to around . The vane pump was turned on at around seconds. The voltage across the microwave diode increased sharply and then appears to decay. The voltage across the diode appears to be related to pressure.

There is some unusual voltage fluctuations observed from to . These points deviate from the trend by about . At seconds the voltage across the diode has a sharp change in voltage of . I was unable to trace any of these abnormalities to any event I observed. Thus, I am assigning any measurements we take to have an error of at least .

Graph 3 shows data taken while the dielectric was in the chamber and the gun was running. This shows the voltage across the microwave diode as a function of time. V3 was set to 0V and V1 was changed between 0V, -2000V, -2990V and -3000V. The graph is color coded according to the voltage V1 was set to. From to we had moved a magnet around to aim the beam over the dielectric. We were able to get the beam over the dielectric. The magnet appeared to have induced some noise. There is no change in voltage when the gun was turned on greater than the error.

 

Spring Analysis

The first step in the analysis process was importing all the data into Matlab, where two functions (see Appendix G) had already been written to help one look for a radiation signal. The first program just took the fast Fourier transform of the data and generated log plots for each data subset (each 100 second on/off part of the cycle, see Appendix F for these plots) as well as for the complete data set.

The figure above shows the fast Fourier transform of the data (power vs frequency)

The second Matlab function computed the phase for each frequency component of the FFT using the relation

where Re[FFT(data)] is the real component of the fast Fourier transform of the data and Im[FFT(data)] is the imaginary part.

The figure above shows the phase plot of the complete data set (see Appendix F for the plots for each data subset).

Since the radiation (if indeed there was any) was being oscillated at 1/100 Hz (once ever 100 seconds), and there is a small peak above the transient slope in the FFT of the signal (this peak is located at approximately 0.02 Hz), the claim that there is indeed radiation present could be made. The phase in that region is uniform, which is a necessary, although not sufficient piece of evidence for a signal that isn't noise. The transient signal is due to the natural downward sloping of the data as time progresses. It should also be noted that the power of the spike associated with the radiation has a power of ~5 x 10^-8 watts. This is just two orders of magnitude below the maximum theoretical value attained by Danos [2]. Of course, the Danos argument makes use of a well-behaved, bunched beam of higher energy. Beam bunching is known to increase the intensity of the radiation, since the radiation induced by a bunched beam radiates coherently. By avoiding altogether the destructive interference within a signal, the signal strength appears higher. In an experiment conducted by Danos [3], he was able to observe ~10^-7 watts of microwave radiation using a very well bunched, but not quite flat beam (4 mm wide by 0.3 mm). Here Danos employed a "klystron-like" bunching cavity to form the pulsed beam.

Summer Data & Analysis

In the summer, the single most important improvement was to rewrite the data acquisition program to record the diode signal with greater precision. By simply modifying the code I was able to improve the precision by three orders of magnitude, from ±1x10^-6 V to ±5x10^-9 V. This resolves the resolution problems that plagued the project in the spring. This puts the experiment in a very good position to observe Cerenkov radiation. To fight the arcing problems that, on many occasions, used to prevent me from reaching the 3000 V needed for Cerenkov radiation, at the end of the spring term the control box was patched (the capacitor's insulation was improved). At the beginning of the summer, the rest of the insulation inside of the control box was thickened for added protection. This was done since, after trials with each of the power supplies individually showed that they were not, on their own, the source of the arcing, the only possible source was the control box. Following the repairs, reaching 3000 V no longer made the system unstable.

The quality of the data sets collected in the summer was only affected by the odd behavior of the diode in the vacuum. Since, after a while, the decline in the voltage from the diode is approximately linear, this affect is not that serious. Below is a plot of the best set of data collected this summer.

By simply subtracting the linear fit of the diode's behavior, the Cerenkov signal can be seen much more easily. Below is such a plot. The red line corresponds to the linear fit for the diode signal before the gun was brought to 3000 V (before the radiation was generated). There was very little variance between this fit for data before the radiation was generated and after the trial was completed. The blue line represents a fit of the data during the periods when the gun was at or above 3000 V (the times when Cerenkov radiation should have been being generated).

One can see that the gun's voltage was modulated (between 2900 V and 3050 V) and that the diode signal responded accordingly. Since the variation was not quite a square function (the changes between 2900 V and 3050 V were not instantaneous) the response was also not square. Eventually I would like to automate the control of the gun's voltage. This way I could generate a cleaner signal, and thus have a more discernable response from the diode.