Session A18 - Superfluid 4He - Vortices and the X Transition.
MIXED session, Monday morning, March 18
Room 241, America's Center

[A18.07] Analytic Calculation of Temperature Error in Sidewall Thermometry Measurements near T_\lambda in ^4He Thermal Conductivity Cells

M. Zofka (University of New Mexico), S.T.P. Boyd (Sandia National Laboratories), V.M. Kenkre (University of New Mexico), R.V. Duncan (Sandia National Laboratories and University of New Mexico)

We report results of a simple analytical calculation of heat flow in a ^4He thermal conductivity cell. The cell has two isothermal anvils which are coaxial with the gravitational field. A coaxial cylindrical shell, or sidewall, of thermal conductivity 20 mWcm^-1K^-1, is between the two anvils and is sealed to them. ^4He is confined inside the vessel formed by the sidewall and the two anvils. We model the temperature field T in the sidewall. Kapitza boundary resistance is set constant. T in the helium column is approximated by the 1-d analytic solution. We model the error of sidewall thermometry \Delta T as the temperature difference between the helium and the outer surface of the sidewall at a height z_probe. When the superfluid interface is well below z_probe, \Delta T is very small. As the superfluid interface moves up in the cell, we find that \Delta T increases sharply over a range of about 0.6 mm to a maximum value, then decreases slowly over about 2 cm to a relatively constant offset when the superfluid interface is well above z_probe. For a heat flux of Q=10^-7 Wcm^-2, \Delta T maximizes at about 40 nK, and goes to a constant value of about 20 nK. We find \Delta T to increase strongly with Q.