ion trap

The physical principles of ion traps were first explored by F. M. Penning (1894–1953), who observed that electrons released by the cathode of an ionization vacuum gauge follow a long cycloidal path to the anode in the presence of a sufficiently strong magnetic field.{{cite journal |title=Die glimmentladung bei niedrigem druck zwischen koaxialen zylindern in einem axialen magnetfeld|author1=F.M. Penning |journal=Physica |volume=3 |pages=873 |year=1936 |doi=10.1016/S0031-8914(36)80313-9 |issue=9}}

A scheme for confining charged particles in three dimensions without the use of magnetic fields was developed by W. Paul based on his work with quadrupole mass spectrometers.

Ion traps were used in television receivers prior to the introduction of aluminized CRT faces around 1958, to protect the phosphor screen from ions.{{cite web |last=Hartson |first=Ted |year=2004 |url=http://www.ieeeghn.org/wiki/images/b/bd/Hartson.pdf |title=How the World Changed Television |access-date=2008-10-13}} The ion trap must be delicately adjusted for maximum brightness.{{US patent|2569517|Magnet for cathode-ray tube ion traps}}{{US patent| 2727171 |Ion Trap for a Cathode Ray Tube}}

File:Paul trap with motion arrows oriented correctly.png. Axial motion (red arrow) is parallel to the radial electrodes and radial motion takes place in the plane given by the green arrows. In a Paul trap, axial motion is confined by a static field and radial motion by the oscillating field. In a Penning trap, axial motion is confined by the static electric field and radial motion is confined by the static magnetic field.]]

Any charged particle, such as an ion, feels a force from an electric or magnetic field. Ion traps work by using this force to confine ions in a small, isolated volume of space so that they can be studied or manipulated. Although any static (constant in time) electromagnetic field produces a force on an ion, it is not possible to confine an ion using only a static electric field. This is a consequence of Earnshaw's theorem. However, physicists have various ways of working around this theorem by using combinations of static magnetic and electric fields (as in a Penning trap) or by an oscillating electric field and a static electric field(Paul trap). Ion motion and confinement in the trap is generally divided into axial and radial components, which are typically addressed separately by different fields. In both Paul and Penning traps, axial ion motion is confined by a static electric field. Paul traps use an oscillating electric field to confine the ion radially and Penning traps generate radial confinement with a static magnetic field.

A Paul trap that uses an oscillating quadrupole field to trap ions radially and a static potential to confine ions axially. The quadrupole field is realized by four parallel electrodes laying in the $z$-axis positioned at the corners of a square in the $xy$-plane. Electrodes diagonally opposite each other are connected and an a.c. voltage $V\; =\; V\_0\backslash cos(\backslash Omega\; t)$ is applied. Using Maxwell's equations, the electric field produced by this potential is electric field $\backslash mathbf\{E\}\; =\; \backslash mathbf\{E\}\_0\backslash sin(\backslash Omega\; t)$. Applying Newton's second law to an ion of charge $e$ and mass $M$ in this a.c. electric field, we can find the force on the ion using $\backslash mathbf\{F\}\; =\; e\backslash mathbf\{E\}$. We wind up with

:$M\backslash mathbf\{\backslash ddot\{r\}\}\; =\; e\backslash mathbf\{E\}\_0\backslash sin(\backslash Omega\; t)\; \backslash !$ .

Assuming that the ion has zero initial velocity, two successive integrations give the velocity and displacement as

:$\backslash mathbf\{\backslash dot\{r\}\}\; =\; \backslash frac\{e\backslash mathbf\{E\}\_0\}\{M\backslash Omega\}\backslash cos(\backslash Omega\; t)\; \backslash !$ ,

:$\backslash mathbf\{r\}\; =\; \backslash mathbf\{r\}\_0\; -\; \backslash frac\{e\backslash mathbf\{E\}\_0\}\{M\backslash Omega^2\}\backslash sin(\backslash Omega\; t)\; \backslash !$ ,

where $\backslash mathbf\{r\}\_0$ is a constant of integration. Thus, the ion oscillates with angular frequency $\backslash Omega$ and amplitude proportional to the electric field strength and is confined radially.

Working specifically with a linear Paul trap, we can write more specific equations of motion. Along the $z$-axis, an analysis of the radial symmetry yields a potential{{cite book | last = Foot | first = Christopher | title = Atomic Physics | publisher = Oxford University Press | location = New York | date = 2005 | page = 259 | isbn = 0198506961}}

:$\backslash phi\; =\; \backslash alpha\; +\; \backslash beta(x^2\; -\; y^2)\; \backslash !$ .

The constants $\backslash alpha$ and $\backslash beta$ are determined by boundary conditions on the electrodes and $\backslash phi$ satisfies Laplace's equation $\backslash nabla^2\backslash phi\; =\; 0$. Assuming the length of the electrodes $r$ is much greater than their separation $r\_0$, it can be shown that

:$\backslash phi\; =\; \backslash phi\_0\; +\; \backslash frac\{V\_0\}\{2r\_0^2\}\backslash cos(\backslash Omega\; t)(x^2\; -\; y^2)\; \backslash !$ .

Since the electric field is given by the gradient of the potential, we get that

:$\backslash mathbf\{E\}\; =\; -\backslash frac\{V\_0\}\{r\_0^2\}\backslash cos(\backslash Omega\; t)(x\backslash mathbf\{\backslash hat\{e\}\}\_x\; -\; y\backslash mathbf\{\backslash hat\{e\}\}\_y)\; \backslash !$ .

Defining $\backslash tau\; =\; \backslash Omega\; t/2$, the equations of motion in the $xy$-plane are a simplified form of the Mathieu equation,

:$\backslash frac\{d^2x\_i\}\{d\backslash tau^2\}\; =\; -\backslash frac\{4eV\_0\}\{Mr\_0^2\backslash Omega^2\}\backslash cos(2\backslash tau)x\_i\; \backslash !$ .

Image:PenningTrapTrajectory.pdf

A standard configuration for a Penning trap consists of a ring electrode and two end caps. A static voltage differential between the ring and end caps confines ions along the axial direction (between end caps). However, as expected from Earnshaw's theorem, the static electric potential is not sufficient to trap an ion in all three dimensions. To provide the radial confinement, a strong axial magnetic field is applied.

For a uniform electric field $\backslash mathbf\{E\}\; =\; E\backslash mathbf\{\backslash hat\{e\}\}\_x$, the force $\backslash mathbf\{F\}\; =\; e\backslash mathbf\{E\}$ accelerates a positively charged ion along the $x$-axis. For a uniform magnetic field $\backslash mathbf\{B\}=\; B\backslash mathbf\{\backslash hat\{e\}\}\_z$, the Lorentz force causes the ion to move in circular motion with cyclotron frequency

:$\backslash omega\_c\; =\; \backslash frac\{eB\}\{M\}\; \backslash !$ .

Assuming an ion with zero initial velocity placed in a region with $\backslash mathbf\{E\}\; =\; E\backslash mathbf\{\backslash hat\{e\}\}\_x$ and $\backslash mathbf\{B\}=\; B\backslash mathbf\{\backslash hat\{e\}\}\_z$, the equations of motion are

:$x\; =\; \backslash frac\{E\}\{\backslash omega\_c\; B\}(1-\backslash cos(\backslash omega\_c\; t))\; \backslash !$ ,

:$y\; =\; -\backslash frac\{E\}\{\backslash omega\_c\; B\}(\backslash omega\_c\; t-\backslash sin(\backslash omega\_c\; t))\; \backslash !$ ,

:$z\; =\; 0\; \backslash !$ .

The resulting motion is a combination of oscillatory motion around the $z$-axis with frequency $\backslash omega\_c$ and a drift velocity in the $y$-direction. The drift velocity is perpendicular to the direction of the electric field.

For the radial electric field produced by the electrodes in a Penning trap, the drift velocity will precess around the axial direction with some frequency $\backslash omega\_m$, called the magnetron frequency. An ion will also have a third characteristic frequency $\backslash omega\_z$ between the two end cap electrodes. The frequencies usually have widely different values with .{{cite book | last = Foot | first = Christopher | title = Atomic Physics | publisher = Oxford University Press | location = New York | date = 2005 | page = 273 | isbn = 0198506961}}

File:Dual linear ion trap.JPG

An ion trap mass spectrometer may incorporate a Penning trap (Fourier-transform ion cyclotron resonance),{{cite journal | title = High-accuracy mass spectrometry with stored ions | author = Blaum, Klaus | journal = Physics Reports | volume = 425 | issue = 1 | pages = 1–78 | year = 2006 | doi = 10.1016/j.physrep.2005.10.011 |bibcode = 2006PhR...425....1B }}

Paul trap{{cite journal | title = Linear ion traps in mass spectrometry | journal = Mass Spectrometry Reviews | author = Douglas, DJ |author2=Frank, AJ |author3=Mao, DM | volume = 24 | issue = 1 | pages = 1–29 | year = 2005 | doi = 10.1002/mas.20004 | pmid = 15389865 | bibcode = 2005MSRv...24....1D }}

or the Kingdon trap.{{cite journal | author=Kingdon KH | title=A Method for the Neutralization of Electron Space Charge by Positive Ionization at Very Low Gas Pressures| journal=Physical Review | volume=21 | pages=408–418 | doi=10.1103/PhysRev.21.408 |year = 1923 | issue=4 |bibcode = 1923PhRv...21..408K }} The Orbitrap, introduced in 2005, is based on the Kingdon trap.{{cite journal | title = The Orbitrap: a new mass spectrometer

| journal = Journal of Mass Spectrometry | year = 2005 | volume = 40 | issue = 4 | pages = 430–443 | last = Hu | first = QZ |author2=Noll, RJ |author3=Li, HY |author4=Makarov, A |author5=Hardman, M |author6= Cooks, RG | doi = 10.1002/jms.856 | pmid = 15838939 |bibcode=2005JMSp...40..430H }} Other types of mass spectrometers may also use a linear quadrupole ion trap as a selective mass filter.

File:IonSpec FT-ICR (Fourier transform Ion cyclotron resonance) Mass spectrometer.jpg

A Penning trap stores charged particles using a strong homogeneous axial magnetic field to confine particles radially and a quadrupole electric field to confine the particles axially.{{cite journal |last1=Brown|first1=L.S.|last2=Gabrielse|first2=G.|title=Geonium theory: Physics of a single electron or ion in a Penning trap|journal=Reviews of Modern Physics|volume=58|issue=1|pages=233–311|year=1986 |url=http://gabrielse.physics.harvard.edu/gabrielse/papers/1986/Review.pdf |bibcode=1986RvMP...58..233B|doi=10.1103/RevModPhys.58.233|access-date=2014-08-09 |archive-url=https://web.archive.org/web/20170313212604/http://gabrielse.physics.harvard.edu/gabrielse/papers/1986/Review.pdf|archive-date=2017-03-13|url-status=dead}} Penning traps are well suited for measurements of the properties of ions and stable charged subatomic particles. Precision studies of the electron magnetic moment by Dehmelt and others are an important topic in modern physics.

Penning traps can be used in quantum computation and quantum information processingHäffner, Hartmut, Christian F. Roos, and Rainer Blatt. "Quantum computing with trapped ions." Physics Reports 469.4 (2008): 155–203. and are used at CERN to store antimatter. Penning traps form the basis of Fourier-transform ion cyclotron resonance mass spectrometry for determining the mass-to-charge ratio of ions.{{cite journal | url=https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=9768511 | pmid=9768511 | date=1998 | last1=Marshall | first1=A. G. | last2=Hendrickson | first2=C. L. | last3=Jackson | first3=G. S. | title=Fourier transform ion cyclotron resonance mass spectrometry: A primer | journal=Mass Spectrometry Reviews | volume=17 | issue=1 | pages=1–35 | doi=10.1002/(SICI)1098-2787(1998)17:1<1::AID-MAS1>3.0.CO;2-K }}

The Penning Trap was invented by Frans Michel Penning and Hans Georg Dehmelt, who built the first trap in the 1950s.{{cite web|title=Hans G. Dehmelt – Biographical|publisher=Nobel Prize |year=1989 |url=https://www.nobelprize.org/nobel_prizes/physics/laureates/1989/dehmelt-bio.html|access-date=June 1, 2014}}

Image:Bruker HCT-schematicJune2008.PNG

A Paul trap is a type of quadrupole ion trap that uses static direct current (DC) and radio frequency (RF) oscillating electric fields to trap ions. Paul traps are commonly used as components of a mass spectrometer. The invention of the 3D quadrupole ion trap itself is attributed to Wolfgang Paul who shared the Nobel Prize in Physics in 1989 for this work.Paul W., Steinwedel H. (1953). "Ein neues Massenspektrometer ohne Magnetfeld". RZeitschrift für Naturforschung A 8 (7): 448–450{{patent|DE|944900|"Verfahren zur Trennung bzw. zum getrennten Nachweis von Ionen verschiedener spezifischer Ladung", W. Paul and H. Steinwedel, filed on December 24, 1953, priority December 23, 1953}} The trap consists of two hyperbolic metal electrodes with their foci facing each other and a hyperbolic ring electrode halfway between the other two electrodes. Ions are trapped in the space between these three electrodes by the oscillating and static electric fields.

File:Orbitrap mass analyzer - partial cross-section.JPG

A Kingdon trap consists of a thin central wire, an outer cylindrical electrode and isolated end cap electrodes at both ends. A static applied voltage results in a radial logarithmic potential between the electrodes. In a Kingdon trap there is no potential minimum to store the ions; however, they are stored with a finite angular momentum about the central wire and the applied electric field in the device allows for the stability of the ion trajectories.{{cite book |last=Major |first=Fouad G. |title=Charged particle traps: physics and techniques of charged particle field |publisher=Springer |year=2005 |isbn=3-540-22043-7}} In 1981, Knight introduced a modified outer electrode that included an axial quadrupole term that confines the ions on the trap axis.{{cite journal|title=Storage of ions from laser-produced plasmas|journal=Applied Physics Letters|year=1981|first=R. D. |last=Knight|volume=38|issue=4|pages=221–223|doi=10.1063/1.92315 |bibcode=1981ApPhL..38..221K}} The dynamic Kingdon trap has an additional AC voltage that uses strong defocusing to permanently store charged particles.{{cite journal |title=Dynamic Kingdon trap |year=1995 |first=R. |last=Blümel |pmid=9911663| journal=Physical Review A| volume=51| issue=1 |pages=R30–R33 |doi=10.1103/PhysRevA.51.R30 |bibcode=1995PhRvA..51...30B}} The dynamic Kingdon trap does not require the trapped ions to have angular momentum with respect to the filament. An Orbitrap is a modified Kingdon trap that is used for mass spectrometry. Though the idea has been suggested and computer simulations performed{{cite journal |journal=International Journal of Mass Spectrometry and Ion Processes |title=A Fourier-transform time-of-flight mass spectrometer. A SIMION calculation approach |author=Oksman, Pentti |volume=141 |issue=1 |date=1995-01-10 |pages=67–76 |doi=10.1016/0168-1176(94)04086-M |bibcode=1995IJMSI.141...67O}} neither the Kingdon nor the Knight configurations were reported to produce mass spectra, as the simulations indicated mass resolving power would be problematic.

{{main|Trapped ion quantum computer}}

Some experimental work towards developing quantum computers use trapped ions. Units of quantum information called qubits are stored in stable electronic states of each ion, and quantum information can be processed and transferred through the collective quantized motion of the ions, interacting by the Coulomb force. Lasers are applied to induce coupling between the qubit states (for single qubit operations) or between the internal qubit states and external motional states (for entanglement between qubits).

• Laser cooling
• Mass spectrometry
• Quantum jump

{{Reflist}}

• [http://www.vias.org/science_cartoons/ion_trap.html VIAS Science Cartoons] A cranky view of an ion trap...
• [http://www.mikomma.de/rotsattel/paulfalle.htm Paul trap]

{{Mass spectrometry}}

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Category:Mass spectrometry

Category:Ions