Copasetic Flow

Summary :  Still More Tensor Identities Three more identities with gradients, divergences, Laplacians, and cross products.  Later today, the fun stuff, special relativity begins! $\vec{A} \cdot \left(\vec{B} \times \vec{C}\right) = \vec{B} \cdot \left(\vec{C} \times \vec{A}\right)$ $= A_i \epsilon_{ijk} B_j C_k$ As long as we only cycle the indices in the Levi-Civita symbol, we won't cause a sign change, so the above is also equal to $= A_k \epsilon_{ijk} B_i C_j$ Which we can commute to get $= B_i \epsilon_{ijk} C_j A_k = \vec{B} \cdot \left(\vec{C} \times \vec{A}\right)$ Done! $\vec{\nabla} \cdot \left(\vec{\nabla} \times \vec{A} \right) = 0$ $=\partial_i \epsilon_{ijk} \partial_j A_k$ $= 0$ If $i$ and $j$ are equal, then the Levi-Civita evaluates to zero.  If they are not equal, then swapping the two indices produces the same mixed partial derivative result, but with a negative sign inserted by swapping indices in the Levi-Civita symbol.  ...

Summary:   Longer spectrum runs were performed on each of the available low energy sources.  The channel vs. energy graph was re-plotted based on the new data.  The behavior is still linear.  The only issue at the moment, is that the signal levels are close to the noise count levels, causing the peaks from each of the sources to be fairly broad.  This should be OK.  since we're just looking for evidence of a signal at all, resolution won't be critical in this application.  The iron magnet cooling supply was completely installed and can supply two gallons per minute to the magnet, meeting the specification.  A Cs 137 Dewar attenuation spectrum was started.  The data will be collected on the morning of the 21 st . Bias 1500 V Gate Window 0.5 uS Threshold 1.5mV Attenuation 0 dB Data set HBC_00015 Source Cs 137 Taped to window Start Time 8:53 AM ...

Summary:  The bias on the PMT was turned to its maximum safe value of 1500 V for maximum gain.  There is a bit of a voltage drop in the PMT base between supply voltage and the anode voltage, so at 1500 V supply voltage, we’re still not running at the maximum rated cathode to anode voltage of 1500 V.  Using peaks from several sources, a channel vs. energy graph was constructed.  Although some of the peaks have small counts and need to be measured more accurately, the linearity looks good with a resolution of about 188 V per channel and a maximum detectable energy of about 203 keV. If you're new to the experiment, scroll to the bottom for background information. Data and Channel vs. Energy Mapping Bias 1500 V Gate Window 0.5 uS Threshold 1.5mV Attenuation 0 dB Data set HBC_00011 Source Am 241 Taped to window Start Time ~ 11:17 ...