The application of the Scott effect to the dynamics of galactic and stellar rotation is investigated. Efforts were also made to improve the sensitivity and stability of torque measurements and understand the microscopic mechanism that causes the Scott effect

Hildebrandt, A. F.

Wood, C. T.

English

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- 2609 7
UNIVERSITY OF HOUSTON
DEPARTMENT OF PHYSICS
FINAL PROGRESS REPORT
July 1, 1971--* -February 29, 1972
-f5* ^ "- FT
«>£*- r •
COPY
THERMOMAGNETIC TORQUES IN POLYATOMIC GASES
NASA GRANT 44-005-122
OFFICE OF GRANTS & RESEARCH CONTRACTS
NASA - OSSA
A. F. Hlldebrandt o T. Wood
https://ntrs.nasa.gov/search.jsp?R=19720018447 2020-03-11T18:06:52+00:00Z
THERMOMAGNETIC TORQUES IN POLYATOMIC GASES
The aim of the work done for the duration of this
grant was to study the Scott effect with specific emphasis
on determining the applicability of the Scott effect to the
dynamics of stellar and galactic rotation. Very simply
stated, one would like to determine the force acting on each
volume element of the gas as a function of the distance to
the center of the system, the gas pressure, the radial ther-
mal gradient, and the vertical magnetic field. The effects'
of the thermomagnetlc torque on a particular system (such as
galaxies or stars) could then be determined by using para-
meters appropriate for the system under consideration. Pro-
gress has been made toward attainment of the final goal. The
work 1s continuing under NASA Grant NGR 44-005-137 and we
feel the goal will be attained.
The work has proceeded according to the following
schemes modification of experimental apparatus to Improve
sensitivity and stability of torque measurements, efforts to
understand the microscopic mechanism which produces the Scott
effect, and formulation of the problem to include treatments
of stellar and galactic systems. The remainder of this
report will be devoted to a discussion of these aspects of
the.-work. .
From the data taken with our present apparatus (see
the Interim Progress Report dated January 1, 1971 - June 30,
' '
1971 for a detailed description of the apparatus), 1t has
been established that several changes needed to be made* In
order to achieve greater stability, the temperature of both
the Inner and outer cylinder had to be controlled and measured.
This change 1s being effected by heating the Inner cylinder
by optical radiation Incident on an absorbing surface. Its
temperature will be measured by a platinum resistance thermo-
meter 1n a bridge circuit. The temperature of the outer
cylinder *1s controlled by use of a water jacket. No change
Is being made 1n this approach. In order to reduce field
2Independent torques (which have been observed by others
 s but
not explained), asymmetries In the system had to be removed.
This change 1s being effected by constructing the water
jacket and outer cylinder out of glass. This eliminates the
need for any glass ports which disrupt the cylindrical sym-
metry and give rise to the field Independent torques. These
field Independent torques were previously conjectured to be
caused by corlolls forces, but have since been found to be a
result of Knudsen effects. A draft of a paper which explains
these field Independent torques and 1s to be submitted to
Physics of Fluids for publication 1s enclosed as part of this
report. The final change which has been made Is the replace-
ment of the solenoid by Helmholtz colls to give greater '
magnetic field homogeneity.
A brief summary of our present understanding of the
Scojtt effect from a microscopic viewpoint is as follows:
(1) If one tries to transform rotational angular momentum
to circumferential angular momentum, the torque Involved 1s
" "
only 10~3 of the observed Scott effect torques. (2) One
might try to Increase the total torque by Increasing the
collision frequency. This would Involve Introducing an
anomalous collision cross section which 1s not observed ex-
perimentally. Support for the previous statement lies 1n the
fact that the expression for the field at which the maximum
torque occurs (Hmax) is given by Hmax = a(P+b)s where a and
b depend on the cross section. No anomalies in a and b are
noted. .'(V) One therefore looks for an anlstropic differen-
tial cross section for scattering of rotating dipoles 1n a
magnetic1 field to get the net chan.ge in angular momentum.
(4) For the pressures at which the Scott effect is observe'd,
binary collisions must account for the effect. Therefore9
one needs to calculate the angular momentum transfer between
two colliding rotating dipoles in a magnetic field and eval-
uate the differential cross section for the collision. The
resulting torque T could be expressed as
omsion (da/dn)dn fV
where AL 1s the angular momentum transferred per collisions '
(da/dJi) 1s the differential scattering cross section,, and t0
is a characteristic relaxation time for correlated scattering ,
in a magnetic field.\ (5) The functional form of TO can be ;
estimated as follows. For; a dilute gas the system will not
be far from equilibrium and the single particle distribution
function for a molecule would be of the form
-. . '.'••'f-V*7*1.^'."''.^.-----'-:-'-'^^'-
:-\v '.;
•\
where fQ Is the equilibrium distribution function ant tx 1s
the collision time (1/ti = apv). If the fourler transform
of e" ' l 1s computed to be
fjRe e - ' e d t = 1/tx
and u) 1s Identified as the frequency 1n the system with
which the collisions must compete (the Larmor frequency In
this case) , then
I/TO:
Since u> > « H (magnetic field) and ti « 1/P.'then
C '
l.'fWP).
The torque measured 1n the Scott effect has the functional
form given above. (6) The preceding arguments suggest that
the quantity of Interest In the Scott effect from a first
principle point of view is the differential scattering cross
section. At the present time we are in the process of eval-
uating the integrals involving AL and da/dn.
As previously stated, the ultimate goal of this work
\
is to study galactic and stellar dynamics which might be
caused by the Scott effect. So far this work has consisted
primarily of gathering evidence to support our position that
the Scott effect may; be applicable to stellar and galactic
systems. The points are listed below:
(1) It is known that stellar systems are composed
s • ' • . ' " - ' -
primarily of molecular hydrogen which does show
a Scott effect.
'".'• Sv.
(2)
(3)
(4)
Thermal gradients are produced by gravitational
contraction. , .
Stellar magnetic fields are large enough to
cause observable Scott effects,
At some time In the formation of a star* the
gas pressures will be of the right order of ;
magnitude for, the Scott effect to be of some 5
Importance. : ; :
REFERENCES
1. G. G. Scott, H. W. Stumer, and R. M; Williamson, Phys*
Rev. 158, 117 (1967). '
2. T i W . Adalr, Private communication.
•»
-t.


Thermomagnetic torques in polyatomic gases

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