cyclotron frequency

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.

• 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.

• 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.

• Period and Frequency

  • The period is the duration of one cycle in a repeating event, while the frequency is the number of cycles per unit time.
  • The frequency is defined as the number of cycles per unit time.
  • Frequency is usually denoted by a Latin letter f or by a Greek letter ν (nu).
  • Note that period and frequency are reciprocals of each other .
  • Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above.

• Beats

  • The wave resulting from the superposition of two similar-frequency waves has a frequency that is the average of the two.
  • This wave fluctuates in amplitude, or beats, with a frequency called the beat frequency.
  • We can determine the beat frequency mathematically by adding two waves together.
  • One can also measure the beat frequency directly.
  • The number of beats per second, or the beat frequency, shows the difference in frequency between the two notes.

• RLC Series Circuit: At Large and Small Frequencies; Phasor Diagram

  • Response of an RLC circuit depends on the driving frequency—at large enough frequencies, inductive (capacitive) term dominates.
  • Now, we will examine the system's response at limits of large and small frequencies.
  • At large enough frequencies $(\nu \gg \frac{1}{\sqrt{2\pi LC}})$, XL is much greater than XC.
  • The impedance Z at small frequencies $(\nu \ll \frac{1}{\sqrt{2\pi LC}})$ is dominated by the capacitive term, assuming that the frequency is high enough so that XC is much larger than R.
  • Distinguish behavior of RLC series circuits as large and small frequencies

• Resonance in RLC Circuits

  • Frequencies at which the response amplitude is a relative maximum are known as the system's resonance frequencies.
  • The reactances vary with frequency $\nu$, with XL large at high frequencies and XC large at low frequencies given as:
  • $\nu_0$ is the resonant frequency of an RLC series circuit.
  • A variable capacitor is often used to adjust the resonance frequency to receive a desired frequency and to reject others. is a graph of current as a function of frequency, illustrating a resonant peak in Irms at $\nu_0 = f_0$.
  • An RLC series circuit with an AC voltage source. f is the frequency of the source.

• Aliasing

  • Looked at from another point of view, for any sampling interval $\Delta$ , there is a special frequency (called the Nyquist frequency), given by $f_s = \frac{1}{2\Delta}$ .
  • The extrema (peaks and troughs) of a sinusoid of frequency $f_s$ will lie exactly $1/2f_s$ apart.
  • Figure 4.9 shows a cosine function sampled at an interval longer than $1/2f_s$ ; this sampling produces an apparent frequency of 1/3 the true frequency.
  • This means that any frequency component in the signal lying outside the interval $(-f_s,f_s)$ will be spuriously shifted into this interval.
  • Figure 4.9: A sinusoid sampled at less than the Nyquist frequency gives rise to spurious periodicities.