Cryogenic Microjet Source for Orthotropic Beams of Ultralarge Superfluid Helium Droplets

Liquid ${}^4\mathrm{H}\mathrm{e}$ at pressures $P_0=0.5–30\mathrm{\text{bars}}$ and temperatures $T_0=1.5–4.2\mathrm{K}$ is discharged into vacuum through two different $2\mu \mathrm{m}$ nozzles. The velocities of the beam of particles obey the Bernoulli equation down to $15\mathrm{m}\mathrm{/}\mathrm{s}\mathrm{e}\mathrm{c}$. With decreasing $T_0$ and increasing $P_0$ the velocity and angular distributions become exceedingly narrow with $\Delta v/v\lesssim 1\%$ and $\Delta \vartheta \lesssim 1\mathrm{m}\mathrm{r}\mathrm{a}\mathrm{d}$. Optical observations indicate that the beam consists of micron-sized droplets ($N\gtrsim {10}^9\mathrm{\text{atoms}}$). This new droplet source provides opportunities for novel experimental studies of superfluid behavior.

Figure 1

The mean beam speeds $v$, relative widths $\Delta v/v$, and angular FWHM $\Delta \vartheta$’s measured with the mass spectrometer set on mass 8 amu as a function of the source temperature $T_0$ at $P_0=3\mathrm{\text{bars}}$ (a)–(c) with the pipette (black circle) and with the orifice (white circle), and as a function of source pressure $P_0$ (d)–(f) at $T_0=1.60\mathrm{K}$ (black circle) and 2.5 K (black square) with the pipette and at $T_0=1.65\mathrm{K}$ (white circle), 2.34 K (triangle), and 4.2 K (diamond) with the orifice. The crosses ($\times$) in (a) and (b) are previous results from Ref. 14 measured with a $5\mu \mathrm{m}$ orifice at $P_0=2.3\pm 0.2\mathrm{\text{bar}}$. Typical TOF and angular distributions, measured at $T_0=1.7\mathrm{K}$, are shown in the insets in (b) and (c) as a dashed line for the orifice and a solid line for the pipette. The arrow in (b) indicates the TOF resolution of the apparatus. The lines in (d) are least-square fits to the Bernoulli equation (see text). Those in (e) and (f) are guides to the eye. The inset in (f) shows the narrowest angular profile measured with the orifice at $P_0=22\mathrm{\text{bars}}$ and $T_0=1.65\mathrm{K}$.

Figure 2

Microscope photograph of the droplet beam with $P_0=3\mathrm{\text{bars}}$ and $T_0=1.7\mathrm{K}$. The beam is illuminated by a halogen lamp off from the line of sight. The nozzle used for the optical observations, located about 2.5 mm behind the 2 cm diameter opening of the outer copper radiation shield (indicated by the white arrow), had a larger diameter of $5\mu \mathrm{m}$.

Figure 3

Schematic diagram showing the two-step model for the state changes accompanying the expansions for $T_0=1.65\mathrm{K}$, $P_0=3\mathrm{\text{bars}}$ ($\alpha =1$), and for $T_0=4.2\mathrm{K}$ at $P_0=15\mathrm{\text{bars}}$ ($\alpha =2$) and $P_0=3\mathrm{\text{bars}}$ ($\alpha =3$). The downward trajectories (thick dashed lines) follow the isentropes (thin dashed lines). The dotted line shows the homogeneous nucleation line based on the standard theory for the present experiments $V\tau \simeq 1.2\times {10}^{-13}{\mathrm{c}\mathrm{m}}^3\mathrm{s}\mathrm{e}\mathrm{c}$ [20]. Since fragmentation is observed for the $\alpha =3$ but not for the $\alpha =2$ trajectory the nucleation line for the helium microjet lies between them and is shifted to lower temperatures.