VOL U ME 4, NU M BE R

P HYSICAL REVI EW LETTERS

FEBRUARY 15, 1960

MEASUREMENT OF THE RED SHIFT IN AN ACCELERATED SYSTEM
USING THE MOSSBAUER EFFECT IN Fe"
H. J. Hay, J. P. Schiffer, T. E. Cranshaw, and P. A. Egelstaff
Atomic Energy Research Establishment, Harwell, England (Received January 27, 1960)

In an adjoining paper' an experiment is described

in which the change of frequency in a photon pass-

ing between two points of different gravitational

potential has been measured. Einstein's principle

of equivalence states that a gravitational field is

locally indistinguishable from an accelerated sys-

tem. It therefore seemed desirable to measure

the shift in the energy of 14-kev gamma rays from Fe'7 in an accelerated system. In order to
do this we have plated a Co" source on to the

surface of a 0.8-cm diameter iron cylinder.

This cylinder was rigidly mounted between two

Dural plates which also held a cylindrical shell

of Lucite, 13.28 cm in diameter and 0.31 cm

thick, concentric with the iron cylinder. An iron
foil 3.5 mg/cm' thick and enriched in Fe" to

50 /0 was glued to the inside surface of the Lucite.

This assembly was mounted in a neutron chopper

drive unit' and rotated at angular velocities up

to 500 cycles per second. The gamma rays

passing through the absorber were detected in a

xenon-f illed proportional counter. A schematic

diagram of the apparatus is shown in Fig. 1.

The expected shift can be calculated in two

ways. One can treat the acceleration as an effec-

tive gravitational field and calculate the difference

in potential between the source and absorber, or

one can obtain the same answer using the time

dilatation of special relativity. The expected

' -8, fractional shift in the energy of the gamma ray

is (fa,',

')GUN/2c' =2.44 x 10 "GUN.

The number of gamma rays as a function of

angular velocity is shown in Fig. 2. In a sep-

arate measurement the counting rate as a func-

tion of radial velocity was determined for this

same source and absorber. It was found that

with the source moving rapidly the counting rate

was 1.29 times what it was with the source sta-

LUCITE

SHAFT DURA

G0UNTER
P LE AY/1
Q yyx~~yx

FIG. 1. Schematic diagram of the experimental
equipment.

Vz Iz 0 I02-
V
aal
I-
aaa IOI-
IK

200

300

400

ANGULAR VELOCITY (revs/Icc)

FIG. 2. Comparison of the calculated curve with
experimental points. The statistical errors of each point are indicated. The curve was calculated from the parameters given in the text.

tionary. The measured full width of the resonance was 0.38 mm/sec. The curve calculated from these parameters is also shown in Fig. 2. The sensitivity of the equipment to vibrations was tested by vibrating the shaft of the rotor with
frequencies corresponding to the rotational fre-
quencies involved, and negligible effect was observed. Changes in counting rate due to forces on the absorber were also found to be negligible.
It appears that the observed effect is in reasonable agreement with expectations. The size of the shift of the gamma-ray energy in the effective gravitational field of a rotating system is in agreement with that due to the terrestrial
gravitational field, within the accuracy of the measurements. The present experiment is expected to be improved when a more pure source is available for reasons stated in the previous paper. It will also be necessary to study further the factors which could influence the absorption process, including changes in the magnetic hyperfine fields due to the high velocities.
We would like to acknowledge helpful and illu-
minating discussions with Dr. J. S. Bell, Dr. W.
Marshall, and Dr. T. Skyrme. We would also like to thank Dr. E. Bretscher for his support
and encouragement.
John Simon Guggenheim fellow, on leave from

165

VOLUME 4, NUMBER 4

PHYSICAL REVIEW LETTERS

FEBRUARY I 5, 1960

J. Argonne National Laboratory, Lemont, Illinois.
T. E. Cranshaw, P. Schiffer, and A. B. White-
head, preceding Letter [Phys. Rev. Letters 4, 163

(1e60)j. J. Egelstaff, Hay, Holt, Baffle, and Pickles, Inst.
Elec. Engrs. (London) (to be published).

STABLE CONFINEMENT OF A HIGH-TEMPERATURE PLASMA
R. F. Post, R. E. Ellis, and F. C. Ford
Lawrence Radiation Laboratory, University of California, Livermore, California
and
M. N. Rosenbluth General Atomic, San Diego, California
(Received January 18, 1960)

Stable, long-time confinement of hot plasma

in a "magnetic bottle" is the ultimate objective

oref tihciaglhl-yt,em'pe~ rtahtuerree

plasma research. Theoare relatively few plasma-

magnetie field configurations which should permit

stable confinement. Even these, when experi-

mentally tested, have until now been found to be

unstable, forcing re-examination and extension

of the theory. We wish in this Letter to report

experiments which represent a contrary example,

providing evidence for the existence of a stably

confined pla, sma, observed under circumstances

where the simplest hydromagnetic theory pre-

dicts instability.

Our two criteria for defining stable confinement

are: (1) The observed confinement time shall

be very much longer than the theoretically pre-

dicted exponentiation time of instabilities. (2)

The rate of escape of the plasma out of the

magnetic bottle shall agree reasonably with that

expected from collisional diffusion (which ulti-

mately limits the attainable time scale for any

mode of plasma confinement).

To satisfy both criteria, the plasma must be

hot and its particle density must not be too high.

This is because rates of diffusion, being pro-

portional to interparticle collision frequencies,

become slower in a plasma the lower is its

density and the higher is its temperature,

whereas hydromagnetic instabilities are pre-

dicted to grow faster the higher the plasma

temperature, at a rate which is essentially

independent of plasma density.

In our experiments the hot plasma was con-

fined in a Mirror Machine' and was produced

by the adiabatic (i. e. , slow) magnetic compression of a low-density burst of hydrogen plasma

injected into the evacuated confinement chamber.

Magnetic comPression ratios (Bfinal/Binitial) of 1000 or more are used, resulting in a spindle

of heated plasma typically 3 or 4 cm in diameter

and about 20 cm in length. The most striking

feature of this plasma is its very high electron

temperature. Following the 500- JL sec compression period
the magnetic field coils are short-circuited, so

that the confining field decays slowly from its

peak value, with a time constant of several

milliseconds.

Preliminary evidence of plasma heating and

long-time confinement in our experiments, first

observed in 1953, was obtained by microwave

methods. Subsequently the spatial and energy

distribution of the confined plasma were meas-

ured and reported. Typical values are:

1.
cm

',Pclaosmmparespsaerdti,cle10de"ntsoity1:0'~incimtial,'.

10" to

10"

2. Plasma electron temperature: initial, 10 ev;

compressed, 10 to 25 kev.

3. Magnetic field: initial, 0 to 100 gauss; final, 10000 to 40000 gauss.

4. Calculated plasma P [pressure —:(B'/8m)]:
up to 0.08.

5. Observed total plasma confinement times:

up to 30 milliseconds (typical half-life at peak

compression, 2 milliseconds).

Confinement times and densities have been

deduced by detection of x rays, by microwave

radiometry and interferometry, by calorimetry,

and by calculation from the initial densities,

and most fruitfully by observing the time depend-

ence of the flux of escaping fast electrons de-

tected by scintillator plus photomultiplier placed

near the magnetic axis outside one of the mirrors.

(See trace of Fig. 1.) Electron temperatures

were determined by absorber foils in front of