The MCP signal calibration measurement uses the MCP threshold signal over range of initial ionization energies for a particular electric field configuration. The red triangles show the threshold MCP signal for an electric field of 4 V/m, which was found using our calibration. The black circles show the threshold MCP signal for an electric field of 9 V/m. The inset figure shows an example of the extrapolation of the trapped electron signal to obtain the MCP threshold signal. The bottom axis of the inset figure shows the number of trapped electrons and the left axis shows the total number of ions and electrons in units of the MCP signal.
An example of the UCP expansion for and total ions. The data are shown as black circles with error bars representing the statistical uncertainty in our measurement of the UCP characteristic size, σ. For clarity the symbol size has been increased, so error bars that are not seen indicate that the uncertainty is less than or equal to the size of the symbol. The red, dashed line shows a self-similar expansion for all of the energy converted to ion expansion energy. The blue, dotted line shows a self similar expansion for 20% of the expansion energy removed during the formation of the UCP. The solid, black line is a fit of the data taking electron evaporation into account throughout the UCP expansion. The post-formation average depth to temperature ratio, for this calculation was found to be 5.4 ± 0.4, 4.7 ± 0.5, and 2.1 ± 0.2 for 25, 50, and 75 K to fit our expansion data. The depths quoted for this data are for electrons assumed to be escaping without any excess energy over the potential well.
An example of our electron evaporation signal for and total ions and electrons.
A plot of the calculated depth to temperature ratio, D/T over a range of temperatures. The open/closed circles show data for a total ion number of ions, respectively. The vertical lines for this data represent the range of depths that were calculated for to of energy removed by each escaping electron for multiple sets of data as described in the text. The depth to temperature ratio shows a sharp decrease at low temperatures that levels off at higher temperatures.
The electron temperature evolution of an expanding ultracold plasma with (solid) and without (dashed) evaporation for . Here, we are looking at the temperature evolution after the UCP formation (starting at 2 μs, where 20% of the energy has been removed). The solid line shows the electron temperature evolution corresponding to the solid, black line from Fig. 2 , whereas the dashed curve shows the temperature evolution for the blue, dotted line in Fig. 2 . It is clear that evaporation lowers the temperature of the electron component at a much faster rate at early times in the evolution, which affects the expansion at later times.
A summary of the influence of electron evaporation on the available UCP expansion energy over a range of conditions. Here we calculate the amount of energy removed from the UCP owing to evaporation that will not be available to drive the ion expansion as described in the text. The first condition shows the model calculations for experimental conditions achievable in our system. The second and third conditions show the calculations for the experimental conditions at higher density found in Refs. 30 and 14 , respectively. The model shows that in general as the density decreases, the influence of electron evaporation on the energy of the UCP increases.
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