View source for Quadrupole ion trap

{{short description|Type of apparatus for isolating charged particles}}
{{Distinguish|Quadrupole mass analyzer}}
[[Image:Paul-Trap.svg|thumb|right|300px|Scheme of a quadrupole ion trap of classical setup with a particle of positive charge (dark red), surrounded by a cloud of similarly charged particles (light red). The electric field {{mvar|E}} (blue) is generated by a quadrupole of endcaps (a, positive) and a ring electrode (b). Picture 1 and 2 show two states during an AC cycle.]]

In [[experimental physics]], a '''quadrupole ion trap''' or '''paul trap''' is a type of [[ion trap]] that uses dynamic [[electric field]]s to trap [[charged particle]]s. They are also called [[radio frequency]] (RF) traps or Paul traps in honor of [[Wolfgang Paul]], who invented the device<ref>Paul W., Steinwedel H. (1953). "Ein neues Massenspektrometer ohne Magnetfeld". RZeitschrift für Naturforschung A '''8''' (7): 448-450</ref><ref>{{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}}</ref> and shared the [[Nobel Prize in Physics]] in 1989 for this work.<ref>{{cite journal |author=Wolfgang Paul |title=Electromagnetic traps for charged and neutral particles |journal=[[Reviews of Modern Physics]] |volume=62 |issue=3 |pages=531–540 |doi=10.1103/RevModPhys.62.531|bibcode = 1990RvMP...62..531P |year=1990}}</ref> It is used as a component of a [[mass spectrometer]] or a [[trapped ion quantum computer]].

== Overview ==
[[File:Paul quadrupole trap.jpg|thumb|250px|Charged flour grains caught in a quadrupole ion trap]]
A charged particle, such as an atomic or molecular [[ion]], feels a force from an [[electric field]]. It is not possible to create a static configuration of electric fields that traps the charged particle in all three directions (this restriction is known as [[Earnshaw's theorem]]). It is possible, however, to create an ''average'' confining force in all three directions by use of electric fields that change in time. To do so, the confining and anti-confining directions are switched at a rate faster than it takes the particle to escape the trap. The traps are also called "radio frequency" traps because the switching rate is often at a [[radio frequency]].

The [[quadrupole]] is the simplest [[electric field]] geometry used in such traps, though [[Multipole expansion|more complicated geometries]] are possible for specialized devices. The electric fields are generated from [[electric potential]]s on metal electrodes. A pure quadrupole is created from [[hyperbola|hyperbolic]] electrodes, though [[Cylinder (geometry)|cylindrical]] electrodes are often used for ease of fabrication. Microfabricated ion traps exist where the electrodes lie in a plane with the trapping region above the plane.<ref>{{cite journal |author=S. Seidelin|title=Microfabricated Surface-Electrode Ion Trap for Scalable Quantum Information Processing |journal=[[Physical Review Letters]] |volume=96 |issue=25 |pages=253003 |doi=10.1103/PhysRevLett.96.253003|display-authors=etal|arxiv = quant-ph/0601173 |bibcode = 2006PhRvL..96y3003S |year=2006|pmid=16907302 |s2cid=9424735 }}</ref> There are two main classes of traps, depending on whether the oscillating field provides confinement in three or two dimensions. In the two-dimension case (a so-called "linear RF trap"), confinement in the third direction is provided by static electric fields.

==Theory==
[[file:Paul Ion Trap Schematic.gif|thumb|]]
The 3D trap itself generally consists of two [[hyperbola|hyperbolic]] metal electrodes with their foci facing each other and a hyperbolic ring electrode halfway between the other two electrodes. The [[ion]]s are trapped in the space between these three electrodes by [[Alternating current|AC]] (oscillating) and [[Direct current|DC]] (static) [[electric field]]s. The AC [[radio frequency]] voltage oscillates between the two hyperbolic metal end cap electrodes if ion excitation is desired; the driving AC voltage is applied to the ring electrode. The ions are first pulled up and down axially while being pushed in radially. The ions are then pulled out radially and pushed in axially (from the top and bottom). In this way the ions move in a complex motion that generally involves the cloud of ions being long and narrow and then short and wide, back and forth, oscillating between the two states. Since the mid-1980s most 3D traps (Paul traps) have used ~1&nbsp;[[Torr|mTorr]] of [[helium]].  The use of damping gas and the mass-selective instability mode developed by Stafford et al. led to the first commercial 3D ion traps.<ref>{{cite journal | last = Stafford | first = G. C. |author2=P. E. Kelley |author3=J. E. P. Syka |author4=W. E. Reynolds |author5=J. F. J. Todd | title = Recent improvements in and analytical applications of advanced ion trap technology | journal = International Journal of Mass Spectrometry and Ion Processes | volume = 60 | issue = 1 | pages = 85–98 | publisher = Elsevier Science B.V. | date = 7 September 1984 | doi = 10.1016/0168-1176(84)80077-4 |bibcode = 1984IJMSI..60...85S }}</ref>

[[Image:lin quad thompson ucalgary.JPG|thumb|300px|right|Linear Ion Trap at the University of Calgary]]
The quadrupole ion trap has two main configurations: the three-dimensional form described above and the linear form made of 4 parallel electrodes. A simplified [[Rectilinear polygon|rectilinear]] configuration is also used.<ref name="pmid15307768">{{cite journal |vauthors=Ouyang Z, Wu G, Song Y, Li H, Plass WR, Cooks RG |title=Rectilinear ion trap: concepts, calculations, and analytical performance of a new mass analyzer |journal=[[Anal. Chem.]] |volume=76 |issue=16 |pages=4595–605 |date=August 2004 |pmid=15307768 |doi=10.1021/ac049420n}}</ref> The advantage of the linear design is its greater storage capacity (in particular of [[Doppler cooling|Doppler-cooled]] ions) and its simplicity, but this leaves a particular constraint on its modeling. The Paul trap is designed to create a saddle-shaped field to trap a charged ion, but with a quadrupole, this saddle-shaped electric field cannot be rotated about an ion in the centre. It can only 'flap' the field up and down. For this reason, the motions of a single ion in the trap are described by [[Mathieu function|Mathieu equations]], which can only be solved numerically by computer simulations.

The intuitive explanation and lowest order approximation is the same as [[strong focusing]] in [[accelerator physics]].  Since the field affects the acceleration, the position lags behind (to lowest order by half a period).  So the particles are at defocused positions when the field is focusing and vice versa.  Being farther from center, they experience a stronger field when the field is focusing than when it is defocusing.

===Equations of motion===

Ions in a quadrupole field experience restoring forces that drive them back toward the center of the trap. The motion of the ions in the field is described by solutions to the [[Mathieu function|Mathieu equation]].<ref name='March 1997'>{{cite journal|last1=March|first1=Raymond E. |title=An Introduction to Quadrupole Ion Trap Mass Spectrometry|journal=Journal of Mass Spectrometry|volume=32 | issue=4 |year=1997 |pages=351–369 | issn=1076-5174 |doi=10.1002/(SICI)1096-9888(199704)32:4<351::AID-JMS512>3.0.CO;2-Y | bibcode=1997JMSp...32..351M |s2cid=16506573 |doi-access=free }}</ref> When written for ion motion in a trap, the equation is

{{NumBlk|:|<math> \frac{d^2u}{d\xi^2}+[a_u-2q_u\cos (2\xi) ]u = 0 </math>|{{EquationRef|1}}}}

where <math>u</math> represents the x, y and z coordinates, <math>\xi</math> is a dimensionless variable given by <math>\xi = \Omega t / 2 </math>, and <math>a_u\,</math> and <math>q_u</math> are dimensionless trapping parameters. The parameter <math>\Omega</math> is the radial frequency of the potential applied to the ring electrode. By using the [[chain rule]], it can be shown that

{{NumBlk|:|<math> \frac{d^2u}{dt^2} = \frac{\Omega^2}{4} \frac{d^2u}{d\xi^2}   </math>|{{EquationRef|2}}}}

Substituting {{EquationNote|2|Equation 2}} into the Mathieu {{EquationNote|1|Equation 1}} yields

{{NumBlk|:|<math> \frac{4}{\Omega^2}\frac{d^2u}{dt^2} + \left[a_u - 2q_u\cos (\Omega t) \right]u = 0 .</math>|{{EquationRef|3}}}}

Multiplying by m and rearranging terms shows us that

{{NumBlk|:|<math> m \frac{d^2u}{dt^2} + m \frac{\Omega^2}{4}\left[a_u - 2q_u\cos (\Omega t) \right]u = 0 .
</math>|{{EquationRef|4}}}}

By [[Newton's laws of motion]], the above equation represents the force on the ion. This equation can be exactly solved using the [[Floquet theorem]] or the standard techniques of [[multiple scale analysis]].<ref>N. W. McLachlan, '''Theory and Applications of Mathieu Functions''' (Oxford University Press, Oxford, 1947), p. 20</ref> The particle dynamics and time averaged density of charged particles in a Paul trap can also be obtained by the concept of [[ponderomotive force]].

The forces in each dimension are not coupled, thus the force acting on an ion in, for example, the x dimension is

{{NumBlk|:|<math>F_x = ma = m\frac{d^2x}{dt^2} = -e \frac{\partial \phi}{\partial x} </math>|{{EquationRef|5}}}}

Here, <math>\phi</math> is the quadrupolar potential, given by

{{NumBlk|:|<math>\phi = \frac{\phi_0}{r_0^2} \bigl( \lambda x^2 + \sigma y^2 + \gamma z^2 \bigr) </math>|{{EquationRef|6}}}}

where <math>\phi _0</math> is the applied electric potential and <math>\lambda </math>, <math>\sigma</math>, and <math>\gamma</math> are weighting factors, and <math>r_0</math> is a size parameter constant. In order to satisfy [[Laplace's equation]], <math>\nabla^2\phi_0 = 0</math>, it can be shown that

:<math> \lambda + \sigma + \gamma = 0 \, . </math>

For an ion trap, <math> \lambda = \sigma = 1 </math> and <math> \gamma = -2 </math> and for a [[quadrupole mass filter]], <math> \lambda = -\sigma = 1 </math> and <math> \gamma = 0 </math>.

Transforming Equation 6 into a [[cylindrical coordinate system]] with <math>x = r \cos\theta</math>, <math>y = r \sin\theta</math>, and <math>z = z </math> and applying the [[Pythagorean trigonometric identity]] <math>\sin^2 \theta + \cos^2 \theta = 1 </math> gives

[[Image:Mass selective instability.gif|right|300 px|thumb|Diagram of the stability regions of a quadrupole ion trap according to the voltage and frequency applied to the ion trap elements.]]

{{NumBlk|:|<math>\phi_{r,z} = \frac{\phi_0}{r_0^2} \big( r^2 - 2z^2 \big) . </math>|{{EquationRef|7}}}}

The applied electric potential is a combination of RF and DC given by

{{NumBlk|:|<math>\phi_0 = U + V\cos \Omega t . </math>|{{EquationRef|8}}}}

where <math>\Omega = 2\pi \nu</math> and <math>\nu</math> is the applied frequency in [[hertz]].

Substituting {{EquationNote|8|Equation 8}} into {{EquationNote|6|Equation 6}} with <math>\lambda = 1</math> gives

{{NumBlk|:|<math> \frac{\partial \phi}{\partial x} = \frac {2x}{r_0^2} \big( U + V\cos \Omega t \big) . </math>|{{EquationRef|9}}}}

Substituting Equation 9 into Equation 5 leads to

{{NumBlk|:|<math> m\frac {d^2x}{dt^2} = - \frac {2e}{r_0^2} \big( U + V\cos \Omega t \big) x . </math>|{{EquationRef|10}}}}

Comparing terms on the right hand side of Equation 1 and Equation 10 leads to

{{NumBlk|:|<math> a_x = \frac {8eU} {m r_0^2 \Omega^2} </math>|{{EquationRef|11}}}}

and

{{NumBlk|:|<math> q_x = - \frac {4eV} {m r_0^2 \Omega^2} . </math>|{{EquationRef|12}}}}

Further <math>q_x = q_y\,</math>,

{{NumBlk|:|<math> a_z = -\frac {16eU} {m r_0^2 \Omega^2} </math>|{{EquationRef|13}}}}

and

{{NumBlk|:|<math> q_z =  \frac {8eV} {m r_0^2 \Omega^2} . </math>|{{EquationRef|14}}}}

The trapping of ions can be understood in terms of stability regions in <math>q_u</math> and <math>a_u</math> space. The boundaries of the shaded regions in the figure are the boundaries of stability in the two directions (also known as boundaries of bands). The domain of overlap of the two regions is the trapping domain. For calculation of these boundaries and similar diagrams as above see Müller-Kirsten.<ref>H.J.W. Müller-Kirsten, Introduction to Quantum Mechanics: Schrödinger Equation and Path Integral, 2nd ed., World Scientific (2012), Chapter 17 on Periodic Potentials, {{ISBN|978-981-4397-73-5}}.</ref>

==Linear ion trap==
{{Expand section|date=May 2008}}
<!-- Deleted image removed: [[File:lin quad Ian Nygren.jpg|right|300 px|thumb]] -->
[[File:Micromotion.png|300px|thumb|Classical motion of a trapped ion in a radiofrequency (rf) quadrupole (Paul) trap. A quadrupole electric field is displayed for reference. The blue line represents the ion path in the transversal (or radial) direction of a linear trap. The orange line is the secular motion. A linear or a circular secular motion can be generated depending on the initial conditions. Micromotion is the fast oscillation around the secular motion, which is enhanced when a stray dc electric field pushes the ion away from the center of the trap, located at the intersection of the axes. Note how the micromotion is always along the direction of the local rf field <ref>{{cite journal |author1= D. J. Berkeland|author2= J. D. Miller|author3= J. C. Bergquist|author4= W. M. Itano|author5= D. J. Wineland | title = Minimization of ion micromotion in a Paul trap | journal = Journal of Applied Physics | volume = 83 | issue = 10 | pages = 5025 | publisher = American Institute of Physics |date=1998 | doi = 10.1063/1.367318}}</ref>]]

[[File:LTQ (Linear trap quadrupole).jpg|thumb|LTQ (Linear trap quadrupole)]]
The [[linear ion trap]] uses a set of quadrupole rods to confine ions radially and a static electrical potential on-end electrodes to confine the ions axially.<ref name="pmid15389865">{{cite journal |vauthors=Douglas DJ, Frank AJ, Mao D |title=Linear ion traps in mass spectrometry |journal=Mass Spectrometry Reviews |volume=24 |issue=1 |pages=1–29 |year=2005 |pmid=15389865 |doi=10.1002/mas.20004|bibcode=2005MSRv...24....1D }}</ref> The linear form of the trap can be used as a selective mass filter, or as an actual trap by creating a potential well for the ions along the axis of the electrodes.<ref>{{cite journal | issue = 1–3| pages = 285–312 | doi=10.1016/S1387-3806(00)00345-6 | volume=200 | title=Quadrupole ion trap mass spectrometry: a view at the turn of the century | year=2000 | journal=International Journal of Mass Spectrometry | last1 = March | first1 = Raymond E| bibcode=2000IJMSp.200..285M }}</ref>  Advantages of the linear trap design are increased ion storage capacity, faster scan times, and simplicity of construction (although quadrupole rod alignment is critical, adding a quality control constraint to their production.  This constraint is additionally present in the machining requirements of the 3D trap).<ref>{{cite journal | last = Schwartz | first = Jae C. |author2=Michael W. Senko |author3=John E. P. Syka | title = A two-dimensional quadrupole ion trap mass spectrometer | journal = Journal of the American Society for Mass Spectrometry | volume = 13 | issue = 6 | pages = 659–669 | publisher = Elsevier Science B.V. |date=June 2002 | doi = 10.1016/S1044-0305(02)00384-7 | pmid = 12056566 | s2cid = 26965687 | doi-access =  }}</ref>

==Cylindrical ion trap==
{{Expand section|date=May 2008}}
[[File:Model of CIT.png|left|thumb|123x123px|The blue lines represents the central cylindrical electrode (ring electrode); the red lines at the top and bottom represent the end-cap electrodes]]
The cylindrical ion trap (CIT) emerged as a derivative of the quadrupole ion trap with simpler geometric structure in which the electrodes are arranged in a cylindrical shape rather than the traditional hyperbolic or linear configuration.<ref name=":0">{{Cite web |last=Tian |first=Yuan |date=2017 |title=Ion Trap Miniaturization Considerations: SpaceCharge Effects in Cylindrical Ion Traps and Misalignment Effects in a Two-Plate Linear Ion Trap |url=https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=7963&context=etd}}</ref> 

The cylindrical ion trap consists of a central cylindrical electrode (ring electrode) and two end-cap electrodes. By applying a combination of static ([[Direct current|DC]]) and oscillating ([[RF]]) voltages to these electrodes, a three-dimensional quadrupole field is generated. The ions are trapped in the center of this field due to the restoring forces created by the electric fields, which confine the ions along the axis and radial directions.<ref>{{Cite book |last=March |first=Raymond E. |url=http://dx.doi.org/10.1002/0471717983 |title=Quadrupole Ion Trap Mass Spectrometry |last2=Todd |first2=John F. J. |date=2005-01-27 |publisher=Wiley |isbn=978-0-471-48888-0}}</ref>

Ion traps with a cylindrical rather than a hyperbolic ring electrode<ref>{{cite journal | last1 = Kornienko | first1 = O. | last2 = Reilly | first2 = P.T.A. | last3 = Whitten | first3 = W.B. | last4 = Ramsey | first4 = J.M. | year = 1999 | title = Micro ion trap mass spectrometry | journal = Rapid Communications in Mass Spectrometry | volume = 13 | issue = 1| pages = 50–53 | doi=10.1002/(sici)1097-0231(19990115)13:1<50::aid-rcm449>3.3.co;2-b| bibcode = 1999RCMS...13...50K }}</ref><ref name="pmid10589092">{{cite journal |vauthors=Ouyang Z, Badman ER, Cooks RG |title=Characterization of a serial array of miniature cylindrical ion trap mass analyzers |journal= Rapid Communications in Mass Spectrometry|volume=13 |issue=24 |pages=2444–9 |year=1999 |pmid=10589092 |doi=10.1002/(SICI)1097-0231(19991230)13:24<2444::AID-RCM810>3.0.CO;2-F }}</ref><ref name="pmid12510732">{{cite journal |vauthors=Patterson GE, Guymon AJ, Riter LS, Everly M, Griep-Raming J, Laughlin BC, Ouyang Z, Cooks RG |title=Miniature cylindrical ion trap mass spectrometer |journal=Anal. Chem. |volume=74 |issue=24 |pages=6145–53 |year=2002 |pmid=12510732 |doi= 10.1021/ac020494d}}</ref><ref name="pmid17672776">{{cite journal |vauthors=Kanawati B, Wanczek KP |title=Characterization of a new open cylindrical ion cyclotron resonance cell with unusual geometry |journal=Review of Scientific Instruments |volume=78 |issue=7 |year=2007 |pages=074102–074102–8 |pmid=17672776 |doi=10.1063/1.2751100|bibcode = 2007RScI...78g4102K }}</ref><ref name="pmid17503946">{{cite journal |vauthors=Cruz D, Chang JP, Fico M, Guymon AJ, Austin DE, Blain MG |title=Design, microfabrication, and analysis of micrometer-sized cylindrical ion trap arrays |journal=Review of Scientific Instruments |volume=78 |issue=1 |year=2007 |pages=015107–015107–9 |pmid=17503946 |doi=10.1063/1.2403840|bibcode = 2007RScI...78a5107C |url=https://zenodo.org/record/1232021 }}</ref> have been developed and microfabricated in arrays to develop [[miniature mass spectrometer]]s for chemical detection in medical diagnosis and other fields. However, the reduction in ion storage volumes remains a problem in small ion traps.<ref name=":0" />

==Planar ion trap==
Quadrupole traps can also be "unfolded" to create the same effect using a set of planar electrodes.<ref name="Seidelin Chiaverini Reichle Bollinger p. ">{{cite journal | last1=Seidelin | first1=S. | last2=Chiaverini | first2=J. | last3=Reichle | first3=R. | last4=Bollinger | first4=J. | last5=Leibfried | first5=D. | last6=Britton | first6=J. | last7=Wesenberg | first7=J. | last8=Blakestad | first8=R. | last9=Epstein | first9=R. | last10=Hume | first10=D. | last11=Itano | first11=W. | last12=Jost | first12=J. | last13=Langer | first13=C. | last14=Ozeri | first14=R. | last15=Shiga | first15=N. | last16=Wineland | first16=D. | title=Microfabricated Surface-Electrode Ion Trap for Scalable Quantum Information Processing | journal=Physical Review Letters | volume=96 | issue=25 | date=2006-06-30 | issn=0031-9007 | doi=10.1103/physrevlett.96.253003 | page= 253003| pmid=16907302 | bibcode=2006PhRvL..96y3003S| arxiv=quant-ph/0601173 | s2cid=9424735 }}</ref> This trap geometry can be made using standard micro-fabrication techniques, including the top metal layer in a standard CMOS microelectronics process,<ref name="Mehta Eltony Bruzewicz Chuang p=044103">{{cite journal | last1=Mehta | first1=K. K. | last2=Eltony | first2=A. M. | last3=Bruzewicz | first3=C. D. | last4=Chuang | first4=I. L. | last5=Ram | first5=R. J. | last6=Sage | first6=J. M. | last7=Chiaverini | first7=J. | title=Ion traps fabricated in a CMOS foundry | journal=Applied Physics Letters | volume=105 | issue=4 | date=2014-07-28 | issn=0003-6951 | doi=10.1063/1.4892061 | page=044103| arxiv=1406.3643 | bibcode=2014ApPhL.105d4103M | s2cid=119209584 }}</ref> and is a key technology for scaling trapped ion quantum computers to useful numbers of qubits.

==Combined radio frequency trap==
A combined radio frequency trap is a combination of a Paul ion trap and a [[Penning trap]].<ref>{{cite journal |author1=J. Walz |author2=S. B. Ross |author3=C. Zimmermann |author4=L. Ricci |author5=M. Prevedelli |author6=T. W. Hansch |year=1996 |title=Confinement of electrons and ions in a combined trap with the potential for antihydrogen production |journal=[[Hyperfine Interactions]] |volume=100 |issue=1 |page=133 |doi=10.1007/BF02059938 |bibcode = 1996HyInt.100..133W |hdl=11572/71547 |s2cid=7625254 |hdl-access=free }}</ref> One of the main bottlenecks of a quadrupole ion trap is that it can confine only single-charged species or multiple species with similar masses. But in certain applications like [[antihydrogen]] production it is important to confine two species of charged particles of widely varying masses. To achieve this objective, a uniform magnetic field is added in the axial direction of the quadrupole ion trap.

== Digital ion trap ==
The [[digital ion trap]] (DIT) is a quadrupole ion trap (linear or 3D) that differs from conventional traps by the driving waveform. A DIT is driven by digital signals, typically rectangular waveforms<ref>{{Cite journal|last1=Brancia|first1=Francesco L.|last2=McCullough|first2=Bryan|last3=Entwistle|first3=Andrew|last4=Grossmann|first4=J. Günter|last5=Ding|first5=Li|date=2010|title=Digital asymmetric waveform isolation (DAWI) in a digital linear ion trap|url=https://pubs.acs.org/doi/10.1021/jasms.8b03836|journal=Journal of the American Society for Mass Spectrometry|language=en|volume=21|issue=9|pages=1530–1533|doi=10.1016/j.jasms.2010.05.003|pmid=20541437|issn=1044-0305|doi-access=free}}</ref><ref>{{Cite journal|last1=Hoffman|first1=Nathan M.|last2=Gotlib|first2=Zachary P.|last3=Opačić|first3=Bojana|last4=Huntley|first4=Adam P.|last5=Moon|first5=Ashley M.|last6=Donahoe|first6=Katherine E. G.|last7=Brabeck|first7=Gregory F.|last8=Reilly|first8=Peter T. A.|date=2018|title=Digital Waveform Technology and the Next Generation of Mass Spectrometers|url=https://pubs.acs.org/doi/10.1021/jasms.8b05747|journal=Journal of the American Society for Mass Spectrometry|language=en|volume=29|issue=2|pages=331–341|doi=10.1007/s13361-017-1807-8|pmid=28971335|bibcode=2018JASMS..29..331H|s2cid=207471456|issn=1044-0305}}</ref> that are generated by switching rapidly between discrete voltage levels. Major advantages of the DIT are its versatility<ref>{{Cite journal|last1=Singh|first1=Rachit|last2=Jayaram|first2=Vivek|last3=Reilly|first3=Peter T.A.|date=2013|title=Duty cycle-based isolation in linear quadrupole ion traps|url=https://linkinghub.elsevier.com/retrieve/pii/S1387380613000730|journal=International Journal of Mass Spectrometry|language=en|volume=343-344|pages=45–49|doi=10.1016/j.ijms.2013.02.012|bibcode=2013IJMSp.343...45S}}</ref> and virtually unlimited mass range. The digital ion trap has been developed mainly as a mass analyzer.

== See also ==
* [[Quadrupole magnet]]

==References==
{{Reflist}}

==Bibliography==
{{refbegin}}
* W. Paul  ''Electromagnetic Traps for Charged and Neutral Particles'' Taken from Proceedings of the International School of Physics <<Enrico Fermi>>  Course CXVIII “Laser Manipulation of Atoms and Ions”, (North Holland, New York, 1992) p.&nbsp;497-517
* R.I. Thompson, T.J. Harmon, and M.G. Ball, ''The rotating-saddle trap<nowiki>:</nowiki> a mechanical analogy to RF-electric-quadrupole ion trapping?'' (Canadian Journal of Physics, 2002: '''80''' 12) p.&nbsp;1433–1448
* M. Welling, H.A. Schuessler, R.I. Thompson, H. Walther  ''Ion/Molecule Reactions, Mass Spectrometry and Optical Spectroscopy in a Linear Ion Trap'' (International Journal of Mass Spectrometry and Ion Processes, 1998: 172) p.&nbsp;95-114.
*{{cite book |author=G. Werth |title=Charged Particle Traps: Physics and Techniques of Charged Particle Field Confinement (Springer Series on Atomic, Optical, and Plasma Physics) |publisher=Springer |location=Berlin |year= 2005|isbn=3-540-22043-7 |oclc= 231588573}}
*{{cite book |author=John Gillaspy |title=Trapping Highly Charged Ions: Fundamentals and Applications |publisher=[[Nova Science Publishers]] |location=Commack, N.Y |year= 2001|isbn=1-56072-725-X |oclc= 42009394}}
*{{cite book |author1=Todd, John F. J. |author2=March, Raymond E. |title=Quadrupole Ion Trap Mass Spectrometry, 2nd Edition |publisher=Wiley-Interscience |location=New York |year= 2005|isbn=0-471-48888-7 |oclc= 56413336}}
*{{cite book |author1=Todd, John F. J. |author2=March, Raymond E. |title=Practical aspects of ion trap mass spectrometry - Volume I: Fundamentals of Ion Trap Mass Spectrometry |publisher=[[CRC Press]] |location=Boca Raton |year=1995 |isbn=0-8493-4452-2 |oclc= 32346425}}
*{{cite book |author1=Todd, John F. J. |author2=March, Raymond E. |title=Practical aspects of ion trap mass spectrometry: Ion Trap Instrumentation, Vol. 2 |publisher=CRC Press |location=Boca Raton |year=1995 |isbn=0-8493-8253-X |oclc= 32346425}}
*{{cite book |author1=Todd, John F. J. |author2=March, Raymond E. |title=Practical aspects of ion trap mass spectrometry, Vol. 3 |publisher=CRC Press |location=Boca Raton |year=1995 |isbn=0-8493-8251-3 |oclc= 32346425}}
*{{cite book |author1=Hughes, Richard M. |author2=March, Raymond E. |author3=Todd, John F. J. |title=Quadrupole storage mass spectrometry |publisher=Wiley |location=New York |year=1989 |isbn=0-471-85794-7 |oclc= 18290778}}
* K. Shah and H. Ramachandran, ''Analytic, nonlinearly exact solutions for an rf confined plasma'', Phys. Plasmas 15, 062303 (2008), ''[https://archive.today/20130223075038/http://link.aip.org/link/?PHPAEN/15/062303/1]
* Pradip K. Ghosh, ''Ion Traps'', International Series of Monographs in Physics, Oxford University Press (1995), ''https://web.archive.org/web/20111102190045/http://www.oup.com/us/catalog/general/subject/Physics/AtomicMolecularOpticalphysics/?view=usa
{{refend}}

===Patents===
* {{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}}
*{{patent|GB|773689|"Improved arrangements for separating or separately detecting charged particles of different specific charges", W. Paul, claims priority of the above German application filed on December 24, 1953}}
* {{patent|US|2939952|"Apparatus for separating charged particles of different specific charges", W. Paul and H. Steinwedel, claims priority of the above German application filed on December 24, 1953}}

==External links==
*[https://web.archive.org/web/20081013004002/http://nobelprize.org/physics/laureates/1989/illpres/ Nobel Prize in Physics 1989]

{{Mass spectrometry}}

[[Category:Mass spectrometry]]
[[Category:Measuring instruments]]
[[Category:German inventions]]
[[Category:Particle traps]]