Charged Particle Traps

Major, F. G.; Gheorghe, V.; Werth, G.

doi:10.1007/b137836

Cited by 28 publications

(46 citation statements)

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“…In particular, the shift must vanish for equal radial amplitudes. This finding is in line with [14,50], where the common root (ρ 2 + −ρ 2 − ) is factored out in the specific expressions for the first few C 2n . We now understand this as a general feature of cylindrically-symmetric electrostatic imperfections.…”

Section: Radial Modessupporting

confidence: 83%

“…For zero amplitude of the radial modes, the only contribution comes from p = 0 and k = 0, and we recover the result from Equation (42) for the one-dimensional case as a little crosscheck. The more comprehensive benchmark is Equation (3.57) in [14] and it agrees. Note that the result is symmetric with respect to the amplitudes of the two radial modes.…”

Section: Axial Modementioning

confidence: 61%

“…Equation (3.56) in [14] provides a crosscheck and there is agreement. By transforming the summation variable according to p → k − p − 1, the exponents of the two radial amplitudes are swapped and we obtain…”

Section: Radial Modesmentioning

confidence: 75%

See 2 more Smart Citations

First-order perturbative calculation of the frequency-shifts caused by static cylindrically-symmetric electric and magnetic imperfections of a Penning trap

Ketter

Eronen

Höcker

et al. 2014

International Journal of Mass Spectrometry

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The ideal Penning trap consists of a uniform magnetic field and an electrostatic quadrupole potential. Cylindrically-symmetric deviations thereof are parametrized by the coefficients Bη and Cη, respectively. Relativistic mass-increase aside, the three characteristic eigenfrequencies of a charged particle stored in an ideal Penning trap are independent of the three motional amplitudes. This threefold harmonicity is a highly-coveted virtue for precision experiments that rely on the measurement of at least one eigenfrequency in order to determine fundamental properties of the stored particle, such as its mass. However, higher-order contributions to the ideal fields result in amplitude-dependent frequency-shifts. In turn, these frequency-shifts need to be understood for estimating systematic experimental errors, and eventually for correcting them by means of calibrating the imperfections. The problem of calculating the frequency-shifts caused by small imperfections of a near-ideal trap yields nicely to perturbation theory, producing analytic formulas that are easy to evaluate for the relevant parameters of an experiment. In particular, the frequency-shifts can be understood on physical rather than purely mathematical grounds by considering which terms actually drive them. Based on identifying these terms, we derive general formulas for the first-order frequency-shifts caused by any perturbation parameter Bη or Cη

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Section: Radial Modessupporting

confidence: 83%

Section: Axial Modementioning

confidence: 61%

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First-order perturbative calculation of the frequency-shifts caused by static cylindrically-symmetric electric and magnetic imperfections of a Penning trap

Ketter

Eronen

Höcker

et al. 2014

International Journal of Mass Spectrometry

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show abstract

“…Probably because of early work on electrons and the interest in their magnetic moment [8], the theoretical treatment of relativistic frequency-shifts used quantum-mechanical operator formalisms [9][10][11][12]. When relativistic equations of motion were considered [13][14][15], the focus was more on excitations of the modified cyclotron-mode than on static frequency-shifts.…”

Section: Introductionmentioning

confidence: 99%

Classical calculation of relativistic frequency-shifts in an ideal Penning trap

Ketter¹,

Eronen²,

Höcker³

et al. 2014

International Journal of Mass Spectrometry

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The ideal Penning trap consists of a uniform magnetic field and an electrostatic quadrupole potential. In the classical low-energy limit, the three characteristic eigenfrequencies of a charged particle trapped in this configuration do not depend on the amplitudes of the three eigenmotions. No matter how accurate the experimental realization of the ideal Penning trap, its harmonicity is ultimately compromised by special relativity. Using a classical formalism of first-order perturbation theory, we calculate the relativistic frequency-shifts associated with the motional degrees of freedom for a spinless particle stored in an ideal Penning trap, and we compare the results with the simple but surprisingly accurate model of relativistic mass-increase

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“…One type of 'hands-on' particle physics experiment that students can perform is the construction of particle traps such as the quadrupole ion trap. Wolfgang Paul and Hans George Dehmelt developed this trap and together were awarded half of the Noble Prize for physics in 1989 for their work [20]. Therefore quadrupole ion traps are often called 'Paul traps' .…”

mentioning

confidence: 99%

3D-Printable Model of a Particle Trap: Development and Use in the Physics Classroom

McGinness¹,

Dührkoop²,

Jansky³

et al. 2019

Journal of Open Hardware

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Quadrupole ion traps are modern and versatile research tools used in mass spectrometers, in atomic frequency and time standards, in trapped ion quantum computing research, and for trapping anti-hydrogen ions at CERN. Despite their educational potential, quadrupole ion traps are seldom introduced into the physics classroom not least because commercial quadrupole ion traps appropriate for classroom use are expensive and difficult to set up. We present an open hardware 3D-printable quadrupole ion trap suitable for the classroom, which is capable of trapping lycopodium spores. We also provide student worksheets developed in an iterative design process, which can guide students while discovering particle traps. The quadrupole ion trap operates using a 3 kV 50 Hz alternating current power supply and uses an astable multivibrator circuit including high luminosity LEDs to illuminate the spores, using the stroboscopic effect to exhibit their movement. The trap can be used in teaching laboratories to enhance high school and university students' understanding of electric fields and their applications.

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Charged Particle Traps

Cited by 28 publications

References 0 publications

First-order perturbative calculation of the frequency-shifts caused by static cylindrically-symmetric electric and magnetic imperfections of a Penning trap

First-order perturbative calculation of the frequency-shifts caused by static cylindrically-symmetric electric and magnetic imperfections of a Penning trap

Classical calculation of relativistic frequency-shifts in an ideal Penning trap

3D-Printable Model of a Particle Trap: Development and Use in the Physics Classroom

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