Simulation of cryogenic buffer gas beams

The cryogenic buffer gas beam (CBGB) is an important tool in the study of cold and ultracold molecules. While there are known techniques to enhance desired beam properties of a CBGB, such as high flux, low velocity, or reduced divergence, they have generally not undergone detailed numerical optimization. Numerical simulation of buffer gas beams is challenging, because the relevant dynamics occur in regions where the density varies by orders of magnitude, rendering typical numerical methods unreliable or intractable. Here we simulate CBGBs with a hybrid approach that combines gas dynamics methods with particle tracing. The simulations capture important properties, such as velocitiy and divergence, across an assortment of designs, including two-stage slowing cells and de Laval nozzles. This approach should therefore be a useful tool for optimizing CBGB designs across a wide range of applications.

Figure 1

Spatial variation of the forward velocity of the 4 K He buffer gas at around 20 SCCM in a single-stage cell computed with DS2V. In this and all other cells, the buffer gas enters on the left and exits through a 5-mm-diameter, 0.5-mm-thick aperture before expanding into vacuum. Gray lines indicate 4 K surfaces.

Figure 2

DSMC results for Mach number $\mathcal{M}$ at the aperture, and corresponding Reynolds number $\mathcal{R}$ [from Eq. (4)], plotted against 4 K He flow (SCCM) for a single-stage cell.

Figure 3

Extraction versus 4 K He flow (SCCM) with three initial conditions: a 1-cm diameter Gaussian ball, 1-cm diameter uniform ball, and uniform distribution over the cell. The initial molecules are thermalized at 4 K. The error bars are calculated using binomial statistics.

Figure 4

Histogram of pumpout times for a 20 SCCM helium flow, or equivalently instantaneous number density at the aperture versus time after the molecules are created. The initial spatial distribution of molecules is a 1 cm diameter Gaussian ball.

Figure 5

Heat map of extraction fraction (top), pumpout time (middle), and diffusion time (bottom) versus initial molecule position for a 20 SCCM buffer gas flow. The $x$ axis indicates the distance from the point where the buffer gas inlet tube ends (0 mm) and finishes at the exit aperture (53 mm). The $y$ axis indicates the radial distance from the central axis of the cell. Therefore, the top right (left) corresponds to the exit aperture (fill line), and the bottom left and right are interior corners. The top figure indicates the symmetry axis (dashed line), as well as the location of the buffer gas inlet, beam exit aperture, and the cell walls. Note that the $x$ and $y$ axes have different scales.

Figure 6

(a) Median forward velocities versus 4 K He flow (SCCM) for SrF mass and various cross sections ${\sigma }_{b-s}$. The dashed and solid lines indicate 4 K He supersonic mean velocity and 4 K SrF thermal velocity, repectively. (b) Median forward velocities versus 4 K He flow (SCCM) for cross section ${\sigma }_{b-s}=3\times {10}^{-14}{\mathrm{cm}}^2$ and various molecular masses. The error bars indicate the standard deviation of the velocity distribution.

Figure 7

Median forward velocities versus distance from the exit aperture for 4 K He with various flow rates (SCCM). The legend indicates flow rate (SCCM) rounded to the nearest integer.

Figure 8

Transverse velocity FWHM and beam divergence versus 4 K He flow (SCCM). The slope of the transverse velocity FWHM at higher flow rates is roughly 0.2 m/s/$\mathcal{R}$, which is consistent with [35, 50].

Figure 9

Spatial variation of the forward velocity of the 4 K He buffer gas at around 20 SCCM in a two-stage cell as computed with DS2V. It consists of the same single-stage buffer gas cell as the previous section with the addition of a slowing cell.

Figure 10

Median forward velocities (top) and extraction fraction (bottom) versus He flow (SCCM) for single-stage (4 K) and two-stage (2 K and 4 K) cells.

Figure 11

Spatial variation of the forward velocity of the 4 K He buffer gas at around 10 SCCM in a cell with a de Laval nozzle, as computed with DS2V.

Figure 12

Beam divergence (top) and transverse velocity spread (bottom) versus 4 K He flow (SCCM) for the straight (standard single-stage) and de Laval apertures.