cyclotron frequency

(noun)

The frequency of a charged particle moving perpendicular to the direction of a uniform magnetic field B (constant magnitude and direction). Given by the equality of the centripetal force and magnetic Lorentz force.

Related Terms

Examples of cyclotron frequency in the following topics:

  • Circular Motion

    • Here, r, called the gyroradius or cyclotron radius, is the radius of curvature of the path of a charged particle with mass m and charge q, moving at a speed v perpendicular to a magnetic field of strength B.
    • A particle experiencing circular motion due to a uniform magnetic field is termed to be in a cyclotron resonance.
    • The term comes from the name of a cyclic particle accelerator called a cyclotron, showed in .
    • The cyclotron frequency (or, equivalently, gyrofrequency) is the number of cycles a particle completes around its circular circuit every second and can be found by solving for v above and substituting in the circulation frequency so that
    • The cyclotron frequency is trivially given in radians per second by

  • Examples and Applications

    • Cyclotrons accelerate charged particle beams using a high frequency alternating voltage which is applied between two "D"-shaped electrodes (also called "dees").
    • To achieve this, the voltage frequency must match the particle's cyclotron resonance frequency,
    • This frequency is given by equality of centripetal force and magnetic Lorentz force.
    • The sizes of the cavities determine the resonant frequency, and thereby the frequency of emitted microwaves.
    • Sketch of a particle being accelerated in a cyclotron, and being ejected through a beamline.

  • Particle Accelerator

    • Oscillating field accelerators, on the other hand, use radio frequency electromagnetic fields to circumvent the breakdown problem.
    • Rolf Widerøe, Gustav Ising, Leó Szilárd, Donald Kerst and Ernest Lawrence are considered pioneers of the field, conceiving and building the first operational linear particle accelerator, the betatron, and the cyclotron.

  • Cumulative Frequency Distributions

    • A cumulative frequency distribution displays a running total of all the preceding frequencies in a frequency distribution.
    • A cumulative frequency distribution is the sum of the class and all classes below it in a frequency distribution.
    • Rather than displaying the frequencies from each class, a cumulative frequency distribution displays a running total of all the preceding frequencies.
    • Constructing a cumulative frequency distribution is not that much different than constructing a regular frequency distribution.
    • The second column should be labeled Frequency.

  • Relative Frequency Distributions

    • To find the relative frequencies, divide each frequency by the total number of data points in the sample.
    • Relative frequency distributions is often displayed in histograms and in frequency polygons.
    • The only difference between a relative frequency distribution graph and a frequency distribution graph is that the vertical axis uses proportional or relative frequency rather than simple frequency.
    • Just like we use cumulative frequency distributions when discussing simple frequency distributions, we often use cumulative frequency distributions when dealing with relative frequency as well.
    • To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row.

  • Frequency of Sound Waves

    • The perception of frequency is called pitch.
    • The perception of frequency is called pitch.
    • The SI unit of frequency is called a Hertz, denoted Hz.
    • Different species can hear different frequency ranges.
    • Three flashing lights, from lowest frequency (top) to highest frequency (bottom). f is the frequency in hertz (Hz); or the number of cycles per second.

  • B.2 Chapter 2

    • We can relate the frequency of the emission to the energy of the electrons and the strength of the magnetic field by
    • Let the frequency of the wave be $\omega$ and the strength of the electric field be E.

  • Do It Yourself: Plotting Qualitative Frequency Distributions

    • Sometimes a relative frequency distribution is desired.
    • Bar graphs for relative frequency distributions are very similar to bar graphs for regular frequency distributions, except this time, the y-axis will be labeled with the relative frequency rather than just simply the frequency.
    • This pie chart shows the frequency distribution of a bag of Skittles.
    • This graph shows the relative frequency distribution of a bag of Skittles.
    • This graph shows the frequency distribution of a bag of Skittles.

  • Guidelines for Plotting Frequency Distributions

    • In statistics, the frequency (or absolute frequency) of an event is the number of times the event occurred in an experiment or study.
    • These frequencies are often graphically represented in histograms.
    • The relative frequency (or empirical probability) of an event refers to the absolute frequency normalized by the total number of events.
    • The height of a rectangle is also equal to the frequency density of the interval, i.e., the frequency divided by the width of the interval.
    • A histogram may also be normalized displaying relative frequencies.

  • Radio Waves

    • The lowest commonly encountered radio frequencies are produced by high-voltage AC power transmission lines at frequencies of 50 or 60 Hz.
    • In this case, a carrier wave having the basic frequency of the radio station (perhaps 105.1 MHz) is modulated in frequency by the audio signal, producing a wave of constant amplitude but varying frequency.
    • Other channels called UHF (ultra high frequency) utilize an even higher frequency range of 470 to 1000 MHz.
    • Frequency modulation for FM radio.
    • (a) A carrier wave at the station's basic frequency.