Thermal and magnetic properties of liquid He3 at low pressure and at very low temperatures

Abstract

A b r ie f review o f the experimental and th eoretical properties o f low pressure liquid He3 as related to the present work is given. This is followed by a d iscussion o f the magnetic cooling method as applied to cooling He3 using both nuclear and electron ic paramagnetics. A number o f possib le metals fo r nuclear cooling are suggested, while cerium magnesium nitrate (dflN) is taken to be the best electronic paramagnetic known fo r the present purposes. The spin-bath thermal resistance is discussed in both cases. In the case o f CMV recent work on the spin-bath r e s i s tance, due to a phonon bottleneck, shows it to be remarkably low. This is borne out in the present experiments. I t is concluded that for temperatures in the m illidegree range CMN is the best p o s s ib il it y. A careful discussion is given o f the techniques developed fo r obtaining and maintaining temperature below 0.010°K fo r many hours in an apparatus o f moderate s iz e using superconducting magnets. D etails are given o f the method o f using epoxy resins for producing apparatus fo r using He3 with application to the measurement o f heat capacity and magnetic prop erties. The method o f executing the experiments is presented together with a thermodynamic analysis o f the effectiv en ess o f the fin a l cooling process. New measurements o f the heat capacity o f a mixture o f low pressure He3 and CM are presented down to a magnetic temperature o f 0.00b°K. No anomalous results are obtained. The experimental technique is analyzed and c r itic iz e d. The resu lts are compared with ea rlier data. The limiting value o f C/nRT s t i l l cannot be p r e c is e ly assessed but seems to be in the range 3 .0 to 3.2°K~. Detailed comparison is made o f the present work with that o f Peshkov, whose resu lts are in terpreted in terms o f an experimental e f f e c t. The thermal boundary resistance from epoxy walls to He3 compares favorably with previous work. Measurements by the spin-echo method o f the s e lf-d iffu s io n c o effic ien t D, and the s u s c e p tib ility. X, o f the He> are presented do™ to a t e v e n W e o f O. m SN o anomalous behavior is observed. D obeys the law D * Work supported by the U.S. Atomic Energy Commission under Contract AT(11-1)-1198.

Active shielding of cylindrical saddle-shaped coils: Application to wire-wound RF coils for very low field NMR and MRI

“…(24). For a coil with k = 1.6554, we find u opt = 60.384°which is consistent with the value u opt = 60.38°quoted by Abel et al [14]. Both of these coil configurations are indicated on the b = 1 curve in Fig.…”

“…The magnetic field of the unshielded saddle-shaped coil has been studied previously by many authors [14][15][16][17][18][19][20][21][22]. For example, Ginsberg and Melchner [15] give the field at the isocenter of the coil and determine conditions for minimizing its second derivatives; Hoult [17] provides an expansion about the isocenter in terms of an infinite series of spherical harmonics; while Hanssum [19] calculates an exact solution in terms of elliptic integrals.…”

“…When k ) 1, u opt = 60°independent of b. The configuration of the unshielded coil noted by Abel et al[14] is indicated by the circle. For the well known configuration (u opt = 60°, k = 2), indicated by the asterisk, all second derivatives of the field are zero at the isocenter[15,16].…”

Principles and methods of dilution refrigeration

“…Extensive measurements of the thermal boundary resistance between either pure He3 or pure He4 and copper have been made by Anderson, Connolly and Wheatley [4 l]. They find that below 100 m°K the thermal boundary resistiv ity between low pressure He3 and electropolished copper is given by (46) while the boundary re sistivity for pure He4 and electropolished copper is less than that given by (46) but increasing relatively as T decreases. The results are summarized on Fig.…”

“…The temperature jump is associated with the large acoustical impedance mismatch between the copper and helium. Now in the case of dilute solutions i f the energy were to be transmitted directly from the walls into collective density modes of the He3 quasiparticles (which have a ll the heat capacity), the acoustic mismatch would be so great that the thermal re sistivity would be orders of magnitude greater than given by equation (46). Thus, at least at high temperatures, i t is most probable that energy is firs t transferred into He4 phonons which then give up energy to the He3 quasiparticles via the He3 quasiparticle-He4 phonon interaction.…”