T(P) calibration

Introduction

One method of calibrating a resistive thermometer in magnetic field over the range \([T_{\min},T_{\max}]\) is to thermally sink the thermometer to a temperature controlled platform which is in turn weakly linked to a constant temperature cryogenic bath at \(T_0\). If the temperature of the platform and the base temperature of the bath are independent of magnetic field strength, then we expect the temperature of the platform to be a magnetic-field-independent function of platform heater power \(P_{\text{heater}}\)
Experimentally, this assumption can be expected to break down
1. if fluctuations in \(T_0\) cause significant changes in \(T_{\text{platform}}\)  at constant \(P_{\text{heater}}\)
2. if the thermal conductance of the 'weak' thermal link is too large or rises too quickly with temperature
3. if ramping of the field changes the temperature of the platform during measurements
Problem 1 is most likely to occur at low T, as \(T_{\min}\rightarrow T_0\), so we require \(T_{\min}\ \gg T_0\).
Problem 2  is most likely to occur at high T, so we require that \(P_{\text{heater}}\)  not exceed the cooling power of the cryogenic bath at the maximum desired value of \(T_0\).
Problem 3 arises from a changing magnetic field, so we require that the magnetic field remain constant as \(P_{\text{platform heater}}\) (and  hence \(T\)) are varied and that the platform and cryogenic system be allowed to return to equilibrium after a change in field prior to ramping the heater power. 
These considerations lead to use of the "bootstrap" method of calibrating resistive thermometers in field, in which \(R(P,B)\) is measured as a function of platform heater power \(P\) while the magnetic field \(B\) is held constant, then repeated for a series of different magnetic field values. The method acquires its name because we first create a functional fit for \(T(P)\) in zero field (using a previously calibrated thermometer), then  use that \(T(P)\) calibration to generate \(R(T,B)\) from R(P,B)\(R(P,B)\), in a method analogous to  booting up a computer by loading the operating system software into the memory, then using that software to take care of loading other software as needed. 
We proceed by using Python to   prepare a calibration of \(P\left(T\right)\) from measurements of \(R\left(P\right)\) and our zero field \(R(T)\) Chebyshev fit.

Python code

calculate T from R

Import zero field \(R\left(P\right)\) data for the calibrated thermometer