Although a chamber made in this way stages a fascinating show, it will not satisfy the serious amateur for long. The tracks- are not easy to see in ordinary light, and old tracks spread into wisps of cloud that soon clutter the view.

Worse yet, the chamber stops working after a few minutes because condensation exhausts the alcohol vapor. To lengthen the operating period a pad saturated with alcohol may be fixed inside the glass top of the upended jar. Vapor evaporating from the pad will keep the chamber going for an hour or more.

The tracks show up best when they are viewed in bright light and against a black background. A 85-millimeter slide-projector may be drafted as the light source; an effective background is provided by a scrap of black velvet fitted to the inside of the jar's screw cap. Old tracks can be cleared from the chamber by mounting a loop of wire just below the glass top and connecting it to the metal bottom through a voltage supply; when the voltage is turned on momentarily, the tracks disappear.

Other accessories may include a camera for photographing the tracks, mirrors set at angles to display the tracks in three dimensions, windows of flat glass to minimize optical distortion, and so on. The succession of improvements follow one another in such easy steps that a novice can find himself immersed in a full-blown hobby almost before he senses his involvement.

That is what happened to Gareth D. Shaw, a field engineer on duty in the Far East for the Bendix Aviation Corporation. His chamber is equipped with a full line of accessories for viewing and photographing tracks, plus other auxiliaries that enable him to identify particles and to determine their mass, charge, energy and velocity.

"All cloud chambers," writes Shaw, "are based on the fact that ions are created when charged particles move through a gas at high speed. Close encounters between the particle and an atom in its path dislodge an electron from the atom. The process forms two ions: the electron itself and the atom, now positive because it has lost a unit of negative charge. Either ion can disturb the delicate balance of electrical forces in a neighboring molecule of alcohol in the vapor state. On close approach to an ion the molecule acquires on the side facing the ion a charge that is opposite in sign to the charge of the ion. In consequence the molecule and the ion are mutually attracted. Other molecules in the vicinity react similarly. The ion thus acts as a center of condensation. When the temperature of the gas is below the dew point of the vapor, a droplet of alcohol quickly forms. A speeding particle leaves thousands of ions in its wake; the resulting droplets comprise the vapor trail.

"Two basic types of cloud chamber have been invented. They differ chiefly in the method used for cooling the gas below the dew point of the vapor. The first type, known as the expansion chamber, takes the form of a cylinder equipped with a close-fitting piston. When the piston is pulled down, the gas expands and its temperature drops. In the second type, the diffusion chamber, the gas is cooled by a refrigerant. When alcohol is used as the condensing vapor, a difference in temperature on the order of 150 degrees Fahrenheit is maintained between the top and bottom of the chamber. Alcohol evaporated near the top diffuses down through the air (or other gas) into the cold region; hence the name diffusion chamber. The amount , of alcohol that can be held in the vapor state by a gas depends directly on the temperature. The cooler air near the bottom of the diffusion chamber has a lower capacity for vapor than the warmer air at the top. Thus an unstable condition arises when alcohol vapor diffuses into the cold region of the chamber. Any small body-for example, a particle of dust-will trigger condensation. The chamber is sealed against the outside air, however, and all the dust in the chamber when it goes into operation is soon carried to the bottom by droplets. Thereafter ions constitute the most likely centers of condensation.

"Dry ice also encourages condensation outside the chamber. This is why it 'smokes.' Water vapor naturally present in the air condenses around particles of suspended dust. The resulting fog can be a source of annoyance, particularly when one is attempting to photograph tracks. In the case of a simple chamber, such as the one shown in the accompanying illustration [Figure 2], fog can be minimized by covering the exposed surfaces of the ice with a towel. Chambers of more sophisticated design, such as one cooled by a slurry of dry ice and alcohol [Figure 3], should be insulated by a jacket of material like that used to cover steam pipes.

"The experimenter is interested in the size and shape of the tracks because they a provide clues to the identity of the responsible particles. It is therefore important to minimize convection currents in the chamber by filtering as much heat from the light beam as possible. A small aquarium with flat sides makes a good filter. Most 35-mm. slide-projectors come equipped with heat filters and blowers. A pair of projectors may be needed to provide enough light for making photographs. Tracks show up best when viewed at an angle of about 130 degrees with respect to the light source.

"Photographs can be made inexpensively with a 35-mm. camera of f/3.5 aperture equipped with an auxiliary lens for close work. Lens openings range from f/3.5 to f/8 and shutter speeds from 1/10 to 1/100 second with film rated ASA 200. The photographs reproduced in this article were made with Kodak Tri-X film and developed in Kodak Microdol, a fine-grain developer. When the light source is relatively weak, a procedure known as 'pushing the film' is possible with this developer. The speed of the film is doubled by doubling the time in which the film is kept in the developer.

"Once the technique of operating the chamber has been mastered, the experimenter should consider adding a magnetic field to it. A chamber without a field is like a yardstick without inch marks-interesting but not very useful. When a charged particle moves at right angles to the direction of a magnetic field, it is acted upon by a force at right angles to both its direction and that of the field. If the field extends in the vertical direction, for example, and the particle moves from east to west, the particle is accelerated in the north-south direction. As a consequence a particle that enters a uniform field follows a circular path [see illustration above]. The radius and direction of the path depend on the sign and magnitude of the charge on the particle, on the mass and velocity of the particle and on the strength and direction of the field.

"A suitable electromagnet can be constructed inexpensively from scrap steel, available in most communities from local industries or scrap dealers. My magnet consisted of two pole-pieces and a yoke made of a pair of plates separated by two rectangular members [see illustration in Figure 4]. The pole-pieces were approximately five inches long. The upper one was machined to a diameter of nine inches and the lower one to a diameter of seven inches. Both were made of soft-steel shafting. In the upper pole-piece was machined a conical hole, which tapered from two inches at the top to five inches at the bottom. The hole provides a clear path for viewing and photographing the tracks. The lower pole-face was shaped to produce a uniform distribution of magnetic flux through the sensitive region of the chamber. The face of this piece is in the form of a shallow, curved cone. The inner edge of the upper pole-face coincides with the center of curvature of the lower pole-face. The radius of curvature in the case of my magnet is four inches ['r' in the illustration]. The pole-pieces are welded to the pair of soft-steel plates, each 8/8 inch thick, 10 inches wide and 18 inches long. The plates are welded in turn to the spacing members, also made of soft steel; each member is 15 inch thick, two inches wide and 14 inches long. The spacers provide an air gap of four inches between the pole-faces.

"Each of the two coils for energizing the magnet consists of 1,000 turns of No. 14 enameled copper magnet-wire, wound on wooden forms and wrapped with insulating tape. The coils require some 60 pounds of wire. The forms were made approximately 1/16 inch larger than the pole-pieces so that the coils could be slipped over the poles easily during assembly. The lower coil rests on the yoke plate and requires no fastening. The upper one is supported by an aluminum ring bolted to the upper pole. The magnet is energized by a six-ampere direct current at 100 volts, and is designed for a maximum duty-cycle of 15 minutes. Extended operation at six amperes results in overheating. The magnet produces a field strength of 1,000 gauss in the sensitive region of the chamber. Motor-generators of the type used for arc welding are suitable for powering the unit and can occasionally be picked up on the surplus market for a few dollars. An inexpensive power supply can also be assembled from surplus rectifier-units of the silicon-disk type.

"The coils must be interconnected so that the current flows in the same direction through each. When they are properly connected, the north end of a magnetic-compass needle will point to one pole-face and the south end to the other. A resistor of 1,000 ohms rated at 20 watts should be connected across the input terminals of the coils to dissipate the energy generated by the collapse of the magnetic field when the magnet is turned off. Without this resistor serious arcing will occur at the switch contacts. If a voltmeter or other instrument is connected across the coils, it should be removed before turning off the magnet; otherwise the sharp rise in voltage that accompanies the collapse of the field will damage the meter.

"When the magnet is ready for operation, the field strength must be measured in the region to be occupied by the sensitive part of the chamber. The current through the coils is adjusted as accurately as possible to six amperes and a note is made of the voltage at this value of current. The field is then measured (in gauss) with a fluxmeter. This measurement is made only once, so a fluxmeter may be borrowed from a local electric-power firm or the physics laboratory of a nearby school. If desired, the magnet may be calibrated for a series of current values.

"The experimenter will be well repaid in terms of convenience for care taken in constructing the chamber. One good design, which is made principally of sheet metal, provides two compartments. The lower one holds the refrigerant (a slurry of crushed dry ice mixed with alcohol), and also serves as the base for the upper compartment. Sheet steel may be used, but copper is recommended at least for the surface between the compartments because of its effectiveness as a conductor of heat. The upper chamber is closed by a lid that consists of an assembly of concentric rings and a disk of clear glass. The ring assembly supports the glass and includes an insulated ring of copper that serves as one electrode for applying an electric field across the chamber to clear it of old tracks. The ring assembly also incorporates a felt pad from which alcohol evaporates when the chamber is in operation. As an alternative scheme the wall of the chamber may be lined with a strip of blotting paper arranged so that its lower edge rests in the pool of alcohol at the bottom of the chamber. Fluid is drawn through the paper by capillary attraction, evaporates, condenses and returns to the pool for re-circulation. The chamber may be supported within the magnet on a flat platform of nonmagnetic sheet metal (such as aluminum) attached to the lower pole. A bracket to support the camera in line with the opening should also be provided.

"To prepare the chamber for operation, crush enough dry ice into pea-sized lumps to fill the lower container. Do not handle the ice with your bare hands-a frozen finger is quite as painful as a burned one. Alcohol is next added slowly to the ice. Violent bubbling may occur until the temperature of the container drops close to that of the ice. Additional ice may be added from time to time as required. Next saturate the pad with alcohol and pour about a tablespoonful of alcohol into the chamber. Place the assembly in the magnet and apply power to the coils.

"Some of the trails in the chamber will now be curved. If the upper pole of the magnet attracts the north end of a magnetic-compass needle (which indicates that the direction of the magnetic flux is from the lower to the upper pole), electrons will follow a counterclockwise path. Relatively light particles of low energy that carry a positive charge will curve clockwise. The direction in which some particles move can be determined by inspection. Energy expended in the creation of ions during flight causes the particle to lose speed; more time is thus available for the transfer of energy near the end of flight. The heavier ionization is seen as a thickening of the track. The direction of flight is known, of course, when particles originate in a radioactive material deliberately placed in the chamber. The identity of some particles can also be determined by inspection. Alpha rays make relatively short, thick tracks; electrons and protons, thin ones. Mesons are usually so energetic that their flight is not perceptibly affected by a field of 1,000 gauss. Consequently their tracks appear thin and straight.

"It is interesting to analyze photographs of tracks and to calculate the speed, mass and energy of the responsible particles. The accompanying photograph [top], for example, shows the circular path of an electron ejected from a short stub of wire coated with radioactive material. Before the photograph was made, the current of the magnet was adjusted to generate a field strength at the chamber of 800 gauss. The momentum of the particle, expressed in units of 'magnetic rigidity,' is equal to the radius of its path multiplied by the field strength. The radius of this particular path is 3.09 centimeters. Thus the momentum of the particle is equal to 3.09 X 800, or 2,472, gauss-centimeters. With this quantity known, the velocity of the particle can be learned by doing just a little more arithmetic. The quantity representing the magnetic rigidity is combined with the ratio of the electron's charge to its mass ( 1.7588 X 10⁷ electromagnetic units per gram) and the velocity of light (3 X 10¹⁰ centimeters per second) according to the accompanying formula [see below]. In this case the velocity turns out to be 2.47 X 10¹⁰ centimeters per second. This is equivalent to about 153,000 miles per second, or 82.4 per cent of the velocity of light. The energy of the particle is found (in millions of electron volts) by squaring the ratio of the velocity of the particle to that of light and inserting the result in the second formula. The energy of the electron in this example was .394 million electron volts.

"An interesting property of matter can be observed by calculating the velocity and energy of a substantial number of electrons and plotting the result as a graph [see Figure 5]. Note how the curve bends up sharply as the speed of the particle approaches the velocity of light This is in accord with the theory of relativity, which states that matter gains mass with velocity, and that the mass becomes in finite at the speed of light. This means that the kinetic energy of a particle, however small it may be, must also increase without limit as it approaches the speed of light, because kinetic energy is the product of mass and velocity.

"A similar graph can be drawn to show how the particle acquires mass with velocity. The mass of the electron at rest is known (it is 9.1 X 10^-28 gram), and its velocity can be measured by means of the diffusion chamber. To find its mass at any velocity these values are inserted in Einstein's equation for relativistic mass [third formula on this page]. The rest is simple arithmetic.

"The curvature of alpha particles is difficult to detect with this apparatus because a magnetic field of 1,000 gauss exerts little influence on their relatively large mass (about 8,000 times that of the electron). The energy of alpha particles can be found by analysis of the tracks, however, because the length of the tracks depends on the rate at which the particles expend energy in ionizing atoms. Curves showing this relationship have been constructed from data acquired: by observing numerous alpha decay processes [see illustration above]. To find the energy of an alpha particle, measure the length of its track in centimeters and refer to the curves. Care must be taken to enlarge the photographs accurately to full scale; errors in enlargement are preserved in the results.

"The classical formula for computing kinetic energy (Ke = 1/2 m v²) may be used for computing the energy of alpha particles because their velocity is so low that the relativistic mass effect may be neglected. This formula expresses energy in terms of ergs. To convert ergs into electron volts multiply by 6.25 X 10¹¹. The length of the alpha track depicted in the second photograph [Figure 8] is 3.1 centimeters, which according to the graph corresponds to an energy of 4.65 mev. From this value the formula for velocity gives a speed of 1.496 X 10⁹ centimeters per second, or about 9,000 miles per second.

"The diffusion chamber invites numerous other interesting experiments. Air can be replaced by other gases, for example. In general it will be found that the quality of the tracks drops in proportion as the molecular weight of the gas falls below that of the vapor. The accompanying photograph of a beta track [Figure 10] was made in an atmosphere of oxygen.

"Gamma rays and X-rays dislodge electrons throughout the gas; the resulting tracks are characteristically erratic [see Figure 11]. In this case a particle source was included and appears at the right side of the picture together with a pattern of alpha tracks. The white strip across the center was made by a wax barrier, inserted to determine whether electrons could penetrate it. The broad, irregular masses in the vicinity of the alpha particles are wisps of cloud representing old tracks. These could have been cleared away by momentarily connecting a potential of from 45 to 90 volts across the electrodes of the chamber."

Bibliography

INTRODUCTORY NUCLEAR PHYSICS. David Halliday. John Wiley & Sons, Inc., 1955.

LECTURE SERIES IN NUCLEAR PHYSICS. E. M. McMillan et al. Government Printing Office, 1947.

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