## Fred's World of Science: Cyclotron I |

Here's a picture of the cyclotron working. The scope shows a wave form that was being picked up by an inductively coupled probe near the driving amplifier. The whole apparatus was set up in the room adjoining my bedroom. That's me crouching in the corner, tuning the amp. To the right is the whole machine, set up for the experiment. This cyclotron only ran air (N2). I was unable to isolate any other species of ions for the experiments. |

These are
pictures of the magnet and its yoke. The yoke was milled to strict
tolerances, and each individual joint of the yoke was welded across the
entire surface area of the joint (that's 25in^{2} of
weld!). |

Here is a slightly clearer view of the operation. You can see the magnet pole pieces (duct taped). You can also see the Al top and bottom and the stainless steel pipe section for the vessel. Please note the "C" clapms. The "C" clamps used here are non-magnetic to prevent any magnetic field distortions. The owners of the hardware store thought I was crazy when I asked specifically non-magnetic "C" clamps. |

This is a picture of the thermocouple gauge I built for the roughing pump side of the vacuum system. The fine blue wire is the Constantan, and the red one is the Iron. I spot welded them together, and then soldered that onto the filament. |

Here's a picture of me tuning the amplifier. On the left is a digital counter I use to select the proper accelerating frequency. On the scope is the output waveform from the RF amplifier. I used a magnetic pickup to isolate the scope from the 1200V plate voltage.

More to come...

In 1931 E. O. Lawrence and M. S. Livingston developed a method of cyclic particle acceleration that produced high energy ions without using a very high voltage source. This accelerator was named the cyclotron. The cyclotron operates on the principle of particle mass resonance. The device uses two hollow "d" shaped electrodes in a vacuum between poles of an electromagnet. To each of the Dees is applied a high-frequency voltage (Lapp 260).

At the center of the Dees there is an ion source producing positive ions. These ions are accelerated into one of the Dees by electrostatic attraction, and when the alternating current shifts from (+) to (-), the ion accelerates into the other Dee. Because of the electromagnetic field, the ion travels in a circular path, and as the ions gain energy their rotational radius increases incrementally, making a spiral orbit. This manner of acceleration continues until the ion escapes from the Dees. "Therefore, as they make revolutions in the Dees, they spiral out into circles of larger radii so that the path length of the ion increases as it gains more energy. The added path length compensates for the increased velocity of the particle" (Lapp, 1962) (Livingston, 1962).

The purpose of this research is to shed light on all phases of construction, analysis, and demonstration of the principles of a small cyclotron. Each piece of equipment and procedure is mine in design origin. I have taken the original plans and schematics and redesigned them to use modern design techniques and components. I have also taken the original calculations, notes, subsequent research and publications available and found modern SI interpretations of the original work for the analysis of my designs and my data. This compilation of work allowed me to study and demonstrate the principle of mass resonance.

For all particles of a certain mass spinning inside a cyclotron one can predict their radius, velocity and frequency using the principle of mass resonance. This principle is based on the concept of centripetal force. One can consider mass resonance calculations as regular force equations with algebraic substitutions to make up for the differences in units. Hence, we must balance centripetal force with magnetomotive force. The centripetal force equation must equal the magnetic force equation, therefore,

Bqv = (mv^{2})/r

where

- B= magnetic field in Teslas
- q = charge of particle in coulombs
- v= velocity of the particle
- m= mass of the particle
- r= radius of particle beam in m

r = mv/Bq

The rotational velocity of the particle (2 pi f) stays constant, while the radius (which is proportional to the ions' energy) increases. Thus the angular velocity of the particle (w) inside a cyclotron is equal to the high-frequency field (expressed as 2 pi f), such that:

w = 2 pi f = v/r

where f is the frequency of the oscillator in cycles/sec. We can substitute this into equation #1 and we get the equation:

f= Bq/ 2 pi m

This is a very useful equation because the f applied to the Dees can be directly related to the m of the ion in question and to the Teslas required of the magnets. (Blanchard, 1958) (Lapp, 1962) (Lawrence, 1948).

Ions do spin and achieve resonance at harmonics of the base frequency of equation #4, but do not complete as many turns in the Dees as at the base f. The harmonic beam makes fewer turns, and thus the E of the beam is less.

With Lawrence's original paper in hand, I set out to demonstrate the principle that made his cyclotron work. I reviewed the plans for his device and adapted his ideas to materials that are now readily available. With resonance as a goal, I compiled a list of equipment I needed. I divided the list into sublists for each separate device, and began designing. Once I had built each of the necessary components, I assembled them on a cart, and began integration. Each component, while working well on its own, had to function as a part of the rather complex whole. Experimentation began after weeks of testing, modifying and retrofitting. Finally, I tested my device under full experimental conditions, with remote controls, high voltage, sensing, and full magnetic flux. I panned through the frequency range of my high voltage supply. Using an oscilloscope and a voltmeter, I recorded the frequencies and target energy change. Lawrence initially used an electroscope to measure relative energy changes. Using the first experiment's data I graphed energy output vs. frequency, and noticed a peak in the data, indicating a probable harmonic resonance point. The second experiment reproduced these results, with the same general peak. The third and fourth experiment showed the same trends in output, confirming that I had achieved resonance. Two of my experiments included plates of film that were exposed inside the chamber. The radiated energy from the beam of ions exposed the film, leaving particle tracks, that were photographed using a camera back microscope. From Eq 4, 5, 6 and 7 I was able to conclude that I was resonating at about a 1/10 up harmonic of the base frequency of resonance of N2.

My data seemed to demonstrate a resonance point, or narrow range
of resonance. The film plates show evidence of radiation, or at least
ions with enough energy to excite the film substrate. Using the frequency
derived from the data, I could substitute numbers into Eq 4 and derive the
mass of the ion accelerated. When I adjusted the frequency by taking into
consideration various harmonics, I found that my data is consistent with
resonance. The resonance graph shows that at a frequency between 2.2 to
2.3 MHz, there is a significant increase in output from the cyclotron.
Above 2.3 MHz there is a dramatic drop in the output, as would be expected
from a resonance curve, or in a Fourier transform analysis. If we take a
1/10 subharmonic of 2.2 MHz and substitute that in Eq 4, we have a mass
of 2.1 x 10^{-26} kg. If we look at the periodic table and take
into
consideration the natural molecular form of gasses, this is close to an
N_{2}^{+} ion. This particular ion would be fairly
common statistically, as it
makes up 78% of any residual air in the evacuated chamber. Although
Nitrogen is fairly electronegative, it is plausible that the ions do
exist. We can also look at a He_{2}^{+} ion and come to
the same general
conclusion. If we take the mass of He_{2}^{+} ion, 6.68 x
10^{-27}
kg, and plug it in to Eq 4 and take a 1/3 up harmonic of the resultant f then we get 2.12 MHz.

Each of these ions would be inside my cyclotron, and could
generate resonance curves consistent with the resonance data. However,
the statistic probability of encountering an He ion, is minuscule compared
to that of N_{2}. Since we cannot predict exactly what ions we
have
inside the chamber, we can only attempt to predict what ions escape, and at what f they will resonate. Therefore, it appears that I achieved mass resonance at a frequency between 2.2 and 2.3 MHz, and that the resonating ions were probably a mixture of elements, the majority of which were likely Nitrogen.

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