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Properties and limitations of an ion guide
Nuclear Instruments and Methods in Physics Research A292 (1990) 45-51 North-Holland
45
PROPERTIES AND LIMITATIONS OF AN ION GUIDE J. SCHELTEN and A. VAN DER HART Institut für Schicht- und Ionentechnik der Kernforschungsanlage Jülich,
D5170 Jülich, Postfach 1413, FRG
Received 16 August 1989 and in revised form 7 February 1990
A flexible electrode hose of 1 m length and with a diameter of 18 mm, consisting of two helically wound wires has been built . Its ability to guide a low-energy Ar ion beam of 1 keV and 100 pA has been tested with electrode potentials up to 500 V . The Smooth Approximation of the equation of motion leads to a focussing effective boundary potential and to a critical glancing angle for ion beam reflection. Similarities with light and neutron guides are discussed. Measurements of the guided ion beam show that the beam is attenuated by atomic charge transfer along the 1 m path due to gas flow from the ion source, that beam losses occur due to fringing fields at the entrance and exit of the guide, which could be prevented in an improved version, and that the defocussing potential caused by the space charge of the low-energy heavy-ion beam diminishes the critical glancing angle severely. With thermal electrons the ion beam cannot be charge-neutralized within the two-wire structure .
l. Introduction
Light guides are well-known devices which are used to transport light over large distances and to distribute light to various places and into various directions . In other applications imaging devices are achieved with glass fibers and information is transported with fiber optics . Neutron guides have been developed for the supply of laboratories outside a reactor hall with thermal- and cold-neutron beams . At the end of a 100 m long neutron guide the background of y-rays and fast neutrons
is drastically reduced . The worldwide total length of light guides and neutron guides is in the order of 100000 and 1 km, respectively. In view of the existence and usefulness of guides for photons and neutrons one might pose the question whether ion guides can be constructed and what they could be used for. In light and neutron guides there is an abrupt change of the refractive index which leads to total refection of rays with glancing angles less than a critical angle. Analogously, one needs for ions a rapid change of the electrostatic potential within a boundary region of the ion guide in order to reflect ion rays. This implies strong electrostatic fields inside a tube. Again, with such fields one would determine a critical glancing angle for ion beam reflections. Photons and neutrons are noninteracting particles while ions interact with each other because of their Coulomb fields . It is this interaction which causes serious difficulties in guiding ions, particularly low-energy heavy ions .
It is the purpose of this paper to describe a testing facility with a 1 m long ion guide, to discuss the equation of motion and approximate solutions which lead to a relation for the critical glancing angle, and to present experimental results on the performance of the ion guide with a 1 keV Ar ion beam. The defocussing potential due to Coulomb interaction is compared with the focussing potential of the ion guide, and experimentally the behaviour of a charge-neutralized beam in the ion guide is investigated . Finally, in evaluating the investigated ion guide in more general terms it should be emphasized that transport lines do exist for ion beams of various energies and currents . In general, the transport elements are magnetic quadrupoles which focus and defocus the beam with linear forces. The beam diameter is changing periodically along the transport line . The theory of such periodic structures with linear forces is well developed. Occasionally transport lines consist of electrical quadrupoles, einzel lenses and bending magnets as lin-
ear transport elements . The main differences between the investigated ion guide and the well-established transport lines are the
following : - do ion guides the focussing forces are extremely nonlinear and influence the beam solely at its boundary . As a consequence, the beam diameter is almost con-
stant . - A theory for beam transport with nonlinear forces has not yet been developed . The investigated ion guide is a flexible transport line which can be bent during operation.
0168-9002/90/$03.50 © 1990 - Elsevier Science Publishers B .V . (North-Holland)
J. Schelten, A. Van der Hart / Properties and limitations of an ion guide
2. Experimental equipment Schematically the testing instrument is shown in fig . 1. It consists of a Kaufman ion source [1] with a 1 cm diameter multi-aperture and a neutralizer filament within the extracted beam, and of two Faraday cups in front and at the end of a 1 m long ion guide for measuring the entrance and exit beam currents. Both Faraday cups are surrounded by negatively biased electrodes for suppressing secondary electrons. The Faraday cup in front of the ion guide can be removed from tl~,e beam. The ion guide is a flexible hose which can be bent to angles up to 30° in order to direct the ion beam into other directions . The ion guide consists of two electrode wires of 1.5 mm diameter, which are helically wound with a pitch of A = 6 mm. Voltages of + V and - V are applied to the two electrodes. The ion guide is constructed by winding the two wires on a double, threaded, 1 m long, hollow rod of 18 mm outer diameter . The wires are held in place by fixing their four ends and by shrinking a plastic hose over the assembly . Thereafter the hollow rod, actually consisting of four 1 m long conically shaped segments, can be removed without destroying the wire structure. With eight spacers the structure °s centered inside a flexible vacuum hose. With two urbomolecular pumps the testing instrument is evacuated . The pressure is in the order of 1 x 10 -6 mbar with no gas flow into the ion source . When the ion source is operating, the pressures are about 1 x 10 -4 and 1 x 10 -5 mbar at the entrance and exit of the ion guide, respectively.
Standard power supplies and amperemeters are used for biasing electrodes and measuring beam currents . 3. Equation of motion A solution of the Laplace equation inside the twowire electrode structure of the ion guide leads to the potential O(r, z) =
(Qa)
V1o (Q ) cos(Qz),
(1)
where a is the aperture radius of the structure, 2%/Q is the electrical periodicity length A, which is twice the distance of two adjacent wires, and V is the applied voltage. An azimuthal dependence can be ignored because of the large value of Qa(= 9.4) . The potentials decrease exponentially towards zero from their boundary values which lie between + V and - V, depending on z. For an ion with a kinetic energy of qU, the equation of motion in the paraxial approximation [2] is d2r = - _V _d Io(Qr) cos(Qz) . 2U dr lo(Qa) dz2 Such an equation cannot be solved analytically. However, the equation can be simplified with the Smooth Approximation [3] by eliminating an oscillatory contribution. The basic idea of the Smooth Approximation is that the solution has a major, slowly varying contribution superimposed by a small, rapidly varying component. For linear differential equations it is shown in ref .
Fig. 1 . Sketch of the testing facility consisting of a multi-aperture source, a 1 an long flexible ion guide, two turbo molecular vacuum pumps, and two Faraday cups for measuring the ion currents before and after the ion guide. The electrical supply consists of : the cathode current I, the discharge voltage Uo, the ion beam voltage U, the accelerator voltage at the second 10 mm diameter grid UA, the current through the neutralizer filament IN , the neutralizer emission current IN., the voltage at the electron suppressor electrode of the first Faraday cup U1, the ion beam current at the entrance of the ion guide I,, the voltages applied to the two ion guide electrodes + V and - V, the voltage at the electron suppressor electrode of the second Faraday cup U,,, and the ion beam current at the end of the ion guide 12. p, and p2 are vacuum pressure meters . Different beam exit directions (3 up to 30 ° can be adjusted by bending the guide hose to curvature radii of 2 m.
J. Schelten, A. Van der Hart / Properties and limitations of an ion guide [3] how the smooth contribution is calculated . For the
nonlinear differential equation (2) one can follow that recipe. In this approximation the equation of motion for the smoothed coordinate is V 21 + d d22 dr (2U) 4 dz
lo(Qr) lo(Qa )
)2
_ 0.
A first integral of this differential equation can be calculated by multiplying eq. (3) with r'. This leads to the critical glancing angle by considering a ray which starts at rt = 0 with the direction rl = ac and is reflected at the boundary, i.e. r2 = a and r2 = 0. The critical-angle relation is
According to eq. (3) the ions move in an effective potential which is almost zero inside the structure and which strongly increases in the vicinity of the boundary. The exponential increase is with an 1/e length of A/4% = 0.5 mm. The height of the effective potential at the boundary is small: Oeff
2
2 _ 1 V
U =aC-8U2)
For U =1000 V and an electrode potential V of 250 V, the effective potential is about 0.8% of the kinetic energy of the ions. It is interesting to compare this effective potential height of an ion guide with the potential barrier heights of light and neutron guides. For Ni-coated-glass neutron guides the potential
47
height is 0.2 t.eV [4), independent of the kinetic energy of the neutrons. For subthermal neutrons of 6.28 A wavelength the relative potential barrier height is only 1 x 10 -4 and even smaller for thermal neutrons. In light guides the abrupt change of the refractive index is wavelength-dependent. If one assumes a 5% refractive-index change in glass fibers one calculates a relative potential barrier height of 1 x 10'1. Thus, the value of 1 x 10 -2 for the ion guide lies between the values of 1 x 10 -4 and 1 x 10' for neutron and light guides, respectively. The equation of motion has been solved numerically. The results confirm the basic idea of the Smooth Approximation that the solution has a small oscillatory contribution superimposed on a smooth trajectory. For beam directions with a < a, and a > ac the probability of reflection closely approaches 1 and 0, respectively. For electrode voltages V larger than U/2 the critical angle does not increase any more with increasing electrode voltage, in contrast to the result of eq. (4) obtained from the Smooth Approximation . A further confirmation of the described motion is obtained from a mechanical model. The profile of the runway represents the r- and z-dependence of the potential as defined in eq. (1) . The sphere model of fig. 2 was constructed with a programmable NC milling machine . For the runway the parameter Qa is 5 instead of 9 .4, which is the value of the ion guide. Nevertheless, one observes reflections of rolling spheres on their slightly oscillating paths. Depending on the glancing angle the sphere is reflected or kicked out of the runway.
sphere. The Fig. 2. Three-dimensional view of the mechanical model with lines emphasizing the profile, and a typical trace of a rolling dimensions are a = 5 cm, A = 6.28 cm and dh = 5 mm . The total length is 0.5 m.
J. Schelten, A. Van der hart l Properties and limitations of an ion guide
48
4. Space charge defocusing In a mean-field approxirnation the Coulomb interaction is described by a beam potential ~ b which is a solution of the Poisson equation:
where p is the charge density of the beam and EO the dielectric constant. Assuming a uniform charge distribution, i.e. a uniform current density at all locations within the guide, the radial dependence of , the beam potential is a parabolic function with its maximum at the beam center. The beam potential can be expressed by 2
~b(r) = D~b 1 - ~ u )
,
(7)
It depends on the beam current I, the kinetic energy qU of the ions, the ion mass M and the relative coordinate r/a . Zo = 377 SZ is the free-space impedance and c the velocity of light . The beam potential drop Orb from center to edge is about 8 V for 1 keV Ar + beam of 60 ~,A . Its relative value is ®~bjU= 0.8 x 10 -Z, identical with the height of the effective potential barrier caused by the electrode structure with an alternating bias of t 250 V. The beam potential lea~3s to a Lnear repulsive force which counteracts the attractive forces caused by the effective potential of the guide. The equation of motion due to both forces is d2r _d _V 2 1 lô(Qr) _ O~b r2 2U a2 dz2 + dr ( 2U ) 4 Î2o( Qa )
From numerical results it has been determined that the voltage V at the guide electrodes should not exceed U/2. With voltages V beyond this limit the amplitude of the oscillatory part of the ion trajectories increases drastically and leads to particle losses. Thus the first term in eq. (10) may be considered ~s being independent of the ion energy qU, provided the electrode voltage can always be set to the same fraction of U. The second term of eq. (10) depends on the mass, energy and current of the ion beam. According to eq. (8) ~~b
a IMt~2Ü-3~2, U i.e. fir 100 times more energetic beams 1000 times more intense beards cans tae guided . rinaiiy, if one is able to compensate the positive charge of the ion beam with thermal electrons either supplied by a hot cathode in the extracted beam or by ionization processes of the ion beam, the repulsive term in eq. (10) is decreased by tkie degree of charge compensation. 5. Experimental results and discussion By measuring the ion beam currents with the second Faraday cup at the end of the straight ion guide for the two ~,ases that the electrodes are grounded and that a voltage of f 250 V is applied to the ion guide electrodes, the transport of ions through the structure is demonstrated . In fig . 3 the guide transmission is plotted versus the ion beam current which enters the ion guide. Ratios of up to 500 have been measured since for
(9)
500 ~
Its first integral determines a new critical glancing angle by again considering a ray which starts at r1 = 0 and ri = a~ and is reflected just at the bounda_a; with r2 f rz and r2 = D. The result is
400 _
1 V 2 z a~ _ ~ ~_~~ ~ m~ -
= 0.
®~b
r~
F_q . (10) has a judicious explanation since a~ is the difference of the relative heights of the attractive and repulsive potentials. There is no reflection if the repulsive interaction exceeds the attractive interaction . The critical glancing angle becomes zero if both interactions are balanced. In general, the space charge term diminishes the critical angle. Zhe discussion of space charge in ion guides is continued with a scaling argument on ion energy and ion current .
300-1 zoo
100 0
T T t 80 100
I~ (uA) Fig. 3. Ratio of the currents Iz at the end of the straight ion guide with and without applied voltages of f 250 V at the guide electrodes versus the ion current h at the entrance of the ion guide. (IN~ = 0, U, _ -100 V and U =1 kV.)
J. Schelten, A. Van der Hart / Properties and limitations ofan ion guide grounded electrodes the current 12 becomes independent of the input current II due to space charge effects, while 12 increases with increasing I, if ±250 V are applied to the electrodes . The very small transmitted current at zero electrode voltages is a consequence of beam divergence and space charge defocussing forces acting in the long and narrow tube of 1 m length and 18 mm diameter. The dependence of the ion beam current at the end of the straight ion guide on the applied voltage at the guide electrodes as shown in fig. 4 behaves qualitatively as one would expect. With increasing voltage the current rises to a saturation value and decreases if the voltage is further increased. This behaviour reflects the increase of of the the ..rcritical. ax agle of reflection with increasing voltage and the particle loss at large applied voltages. In fig. 5 it is shown that an ion beam is transported through bent guides . The amount of bending of the 1 m long ion guide is determined by the angle of beam deflection. At zero applied voltage the ion beam current at the end of the bent ion guide is zero and raises to a saturation value with increasing applied voltage. The more the guide is bent, the more voltage is needed for guiding the beam. This result is again qualitatively in agreement with the critical angle dependence of eq. (4).
49
10 987654 3 1 0 Fig. 5. Ion current 12 at the end of the ion guide versus the applied voltage at the ion guide electrodes. Parameter of the curves is the curvature of the ion guide hose, indicated by the beam exit direction angle ß. (1, = 30 pA, INe =10 mA, U1 -100 V, U =1 kV.)
9-
However, the quantitative analysis of these results will indicate that the ion guide is far from ideal . A guide is called ideal if all. rays with glancing angles less than a critical angle are being reflected and transported through a guide of any length . Light and neutron guides are almost ideal. The ion guide behaves non-ideally because of attenuation, fringing field effects, space charge and lack of charge neutralization.
8-
5.1 . Attenuation
7-
Various collision processes can occur between the 1 keV Ar ions and the Ar gas atoms during the 1 m long flight path in the ion guide . Ion momentum and energy are changed in elastic collisions, while in inelastic collisions mainly the ion energy changes. In such processes the gas atoms become excited or even ionized, or a charge transfer takes place [5] . In those experiments the most probably process is the one of charge transfer where an energetic atom and a thermal ion are generated. For the beam current measurements at the end of the ion guide the process appears as attenuation of the beam. The attenuation factor is
12
0'-* 11 =100pA
11 10-
65-
41
x~x-x-x_I, ~x-x_x `x
3-
=10 uA
x1
2 1
x/~
0
100
200 300 400 500 V± (VI Fig. 4. Ion current 12 at the end of the straight ion guide versus the applied voltage at the guide electrodes . Parameter of the curves is the entrance current fI . U Ne = 0, SI1 = --100 V and U ='1 kV.)
pl (12) ( pl)o where the pressure- path-length product( pl )o for charge -a transfer of 1 keV Ar ions with Ar atoms is 2.0 x 1V -a mbar m [1]. This means that at a pressure of 1.4 x 10 T = exp -
50
J. Schelten, A . Van der Hart / Properties and limitations of an ion guide are large enough in order that the ion ray overcomes the small effective attractive potential from the alternating fields inside the guide, i.e. the deflected rays get lost. A solution to this problem would be an adiabatic onset of the guide fields. This can be achieved by slowly increasing the electrode voltage over quite a number of windings . Another more practical measure would be to shape the guide conically at both ends. For the testing experiments the aperture of the suppressor electrode in front
Fig. 6 . Semi-log plot of the ion beam current 12 at the end of the straight ion guide versus pressure pl in front of the ion guide. At the usual working condition marked by the arrow, the attenuation due to atomic charge transfer is 5056 . (11= 50 IL A, IN. = 0, U1 = -100 V, U =1 kV .)
of the guide was narrowed in order that only ions which are close to the guide axis (r :5 a/2) can enter the guide. At the other end of the guide the Faraday cup was placed very close to the guide exit in order that also ions deflected by the exit fringing fields can reach the second Faraday cup. By this measure the current ratio 12/11 was doubled and the experimental results became interpretable. 5.3. Space charge
mbar in the 1 m long guide the ion beam is attenuated by a factor of 0 .5 . The beam attenuation is experimentally verified by measuring the beam current 12 as a function of the gas pressure pt at the entrance of the guide. Typical results are shown in fig. 6 . The straight line is the log-lin plot corresponding to a (p1 1 )o value of 3 .5 x 10 -4 mbarm. Since the pressure pt is larger than p2 and the pressure inside the guide due to gas flow from. the ion source, this result is in close agreement with the well-known pressure-path-length product (pl )o of 2 .0 x 10 -4 mbar m . However, more important than this agreement is that one gets the attenuation factor under operation conditions, which usually was at a pressure pt marked by the arrow in fig . 6. At this pressure the measured attenuation factor is 0.5 . Its value hardly changes by increasing the ion current fed into the ion guide, by biasing the guide electrodes, or by neutralizing the beam . For a quantitative evaluation of the ion guide this attenuation factor was taken into account .
For the simplest space charge model, based on a constant charge density across and along the guide, a critical angle of reflection, ac was calculated in section 4. According to this model, a,2 varies linearly with the transported current. For a given ion energy, ion mass and electrode voltage V it holds c apt% 2 = a (0) 2 1 - 1s
13)
,
where 1t is the transported current and aß (0) is the a, of eq. (4) . The critical angle vanishes if the maximum current Im is reached .
0,a-
5.2. Fringing field effects In the theoretical section, infinitely long ion guides were treated. lil:aL the Lbeath experiments a ï m long ion guide is tested which has an entrance and an exit . Preliminary experiments have shown that a large fraction of the beam entering the guide gets lost . This loss is caused by the field of the potentials of the outer two half windings . The field expands into the entrance region and is much larger than the field inside the guide. The fringing fields are strongest at a distance r = a from the axis . As a consequence, the entering beam is deflected by this field and in particular that part of the beam which is away from the axis. The deflection angles
0,2
20
40
60
80
100
Fig . 7. Ion current 12 at the end of the straight ion guide with a voltage of t 250 V applied to the guide electrodes versus the entrance ion current h . The current 12 is normalized to T times 11 , where T is the attenuation factor due to atomic charge transfer. The solid curve is a model function with one adjusted parameter. (IN, = 0 mA, U1 = -100 V, U =1 kV.)
J. Schelten, A. Van der Hart / Properties and limitations of an ion guide
The current fed into this solid angle aj It )2 is a fraction of the entrance current : ( 2 I,== I1 Min~ 1, (14)
12
aD )
10
D
where a D is the divergence of the beam at the entrance of the guide . By inserting eq. (13) into eq. (14) one obtains jl
= Min 1,
[I
+
a
a
2 -1
51
a ôV
V* = 0 6
(15)
If one identifies the transported current with I2 /T, which is the attenuation-corrected current at the end of the ion guide, sets Im = 60 pA according to the values of section 4 for an electrode voltage of ±250 V, and assumes aD/a.(0) = 0.9, one obtains the curve in fig. 7 which in general describes the Il dependence of the measured data. One should not expect a better agreement because of the simplifications made in the model. Note for instance, that the current decreases by an order of magnitude along the guide in the experiment while the model assumes a transported current which stays constant along the guide . Nevertheless, the experimental data clearly demonstrate that the space charge of the ion beam is responsible for the small fraction of input current which can be transported by the ion guide. 5.4. Neutralization
If enough electrons are generated by the heated neutralizer filament in the extracted ion beam, the beam becomes at least partly neutralized. As a consequence, the repulsive term in eq. (10) is diminished. Inside the guide the thermal electrons see the strong, exponentially decaying field with inward and outward radial directions depending on position z. Although the fields are strong only near the boundary and almost zero near the axis, the experimental result of fig. 8 seems to indicate that all electrons are pulled out of the ion guide. This suggestion is qualitatively confirmed by the observed current at the positively biased electrode. When a voltage of f 260 V is applied to the electrodes, the current 12 is not influenced by the electron supply as indicated " e .t_ __ L_ s_-___ r_" _ by the lower curve min llg. C. FlUWGVGr, 11 Llle G1e%:Ll VUVJ are grounded and electrons are supplied, the ion beam remains partly charge-neutralized on its way to the second Faraday cup since the current 12 rises by a factor between 5 and 12 according to the upper curve of fig . 8. A quantitative analysis of the currents h atid 12 demonstrates that the larger the entrance current, the less the beam is charge-neutralized .
2
V. - 260V o-o--~-o-o- 0-o_o o-o--.o 1 100
Fig. 8. Ratio of ion currents at the end of the staight ion guide versus the entrance current 11 . Parameter is the applied electrode voltage . I"P and I2°°°'P are the currents with an abundance of charge-neutralizing electrons (IN, =10 MA, U1 = 0 V) and without an electron supply (INe = 0, U1 = -100 V), respectively.
In summary it can be stated that for 1 keV Ar ion beams the ion guide is far from ideal, mainly because of repulsive space-charge forces. Thermal electrons provided to charge-neutralize the beam are withdrawn in the ion guide. Acknowledgements We are grateful to U. Kurz and W. Reimer for designing the test facility and to J. Zillikens for the construction of the flexible ion guide and the assembly of the test facility, and for his assistance during the measurements. We thank Dr. R. Lehmann and Dr. M. Pabst for stimulating discussions. References Ion-Source Operation (Commonwealth Scientific Corporation, 1984). P. Grivet, Electron Optics (Pergamon, 1972) p. 95 ff. H. Bruck, Accélérateurs Circulaires de Particules, Chap. IX (Presses Universitaires de France, 1966). B. Alefeld, J. Christ, D. Kukla, R. Scherm and W. Schmatz, JÜL 294-NP (1965) . H. Neuert, Atomare Stossprozesse (Teubner Studienbücher, Physik. 1984).
[il H.R_ Kaufman_ Fundamentals of
[2] [3 1, [4] [5]
45
PROPERTIES AND LIMITATIONS OF AN ION GUIDE J. SCHELTEN and A. VAN DER HART Institut für Schicht- und Ionentechnik der Kernforschungsanlage Jülich,
D5170 Jülich, Postfach 1413, FRG
Received 16 August 1989 and in revised form 7 February 1990
A flexible electrode hose of 1 m length and with a diameter of 18 mm, consisting of two helically wound wires has been built . Its ability to guide a low-energy Ar ion beam of 1 keV and 100 pA has been tested with electrode potentials up to 500 V . The Smooth Approximation of the equation of motion leads to a focussing effective boundary potential and to a critical glancing angle for ion beam reflection. Similarities with light and neutron guides are discussed. Measurements of the guided ion beam show that the beam is attenuated by atomic charge transfer along the 1 m path due to gas flow from the ion source, that beam losses occur due to fringing fields at the entrance and exit of the guide, which could be prevented in an improved version, and that the defocussing potential caused by the space charge of the low-energy heavy-ion beam diminishes the critical glancing angle severely. With thermal electrons the ion beam cannot be charge-neutralized within the two-wire structure .
l. Introduction
Light guides are well-known devices which are used to transport light over large distances and to distribute light to various places and into various directions . In other applications imaging devices are achieved with glass fibers and information is transported with fiber optics . Neutron guides have been developed for the supply of laboratories outside a reactor hall with thermal- and cold-neutron beams . At the end of a 100 m long neutron guide the background of y-rays and fast neutrons
is drastically reduced . The worldwide total length of light guides and neutron guides is in the order of 100000 and 1 km, respectively. In view of the existence and usefulness of guides for photons and neutrons one might pose the question whether ion guides can be constructed and what they could be used for. In light and neutron guides there is an abrupt change of the refractive index which leads to total refection of rays with glancing angles less than a critical angle. Analogously, one needs for ions a rapid change of the electrostatic potential within a boundary region of the ion guide in order to reflect ion rays. This implies strong electrostatic fields inside a tube. Again, with such fields one would determine a critical glancing angle for ion beam reflections. Photons and neutrons are noninteracting particles while ions interact with each other because of their Coulomb fields . It is this interaction which causes serious difficulties in guiding ions, particularly low-energy heavy ions .
It is the purpose of this paper to describe a testing facility with a 1 m long ion guide, to discuss the equation of motion and approximate solutions which lead to a relation for the critical glancing angle, and to present experimental results on the performance of the ion guide with a 1 keV Ar ion beam. The defocussing potential due to Coulomb interaction is compared with the focussing potential of the ion guide, and experimentally the behaviour of a charge-neutralized beam in the ion guide is investigated . Finally, in evaluating the investigated ion guide in more general terms it should be emphasized that transport lines do exist for ion beams of various energies and currents . In general, the transport elements are magnetic quadrupoles which focus and defocus the beam with linear forces. The beam diameter is changing periodically along the transport line . The theory of such periodic structures with linear forces is well developed. Occasionally transport lines consist of electrical quadrupoles, einzel lenses and bending magnets as lin-
ear transport elements . The main differences between the investigated ion guide and the well-established transport lines are the
following : - do ion guides the focussing forces are extremely nonlinear and influence the beam solely at its boundary . As a consequence, the beam diameter is almost con-
stant . - A theory for beam transport with nonlinear forces has not yet been developed . The investigated ion guide is a flexible transport line which can be bent during operation.
0168-9002/90/$03.50 © 1990 - Elsevier Science Publishers B .V . (North-Holland)
J. Schelten, A. Van der Hart / Properties and limitations of an ion guide
2. Experimental equipment Schematically the testing instrument is shown in fig . 1. It consists of a Kaufman ion source [1] with a 1 cm diameter multi-aperture and a neutralizer filament within the extracted beam, and of two Faraday cups in front and at the end of a 1 m long ion guide for measuring the entrance and exit beam currents. Both Faraday cups are surrounded by negatively biased electrodes for suppressing secondary electrons. The Faraday cup in front of the ion guide can be removed from tl~,e beam. The ion guide is a flexible hose which can be bent to angles up to 30° in order to direct the ion beam into other directions . The ion guide consists of two electrode wires of 1.5 mm diameter, which are helically wound with a pitch of A = 6 mm. Voltages of + V and - V are applied to the two electrodes. The ion guide is constructed by winding the two wires on a double, threaded, 1 m long, hollow rod of 18 mm outer diameter . The wires are held in place by fixing their four ends and by shrinking a plastic hose over the assembly . Thereafter the hollow rod, actually consisting of four 1 m long conically shaped segments, can be removed without destroying the wire structure. With eight spacers the structure °s centered inside a flexible vacuum hose. With two urbomolecular pumps the testing instrument is evacuated . The pressure is in the order of 1 x 10 -6 mbar with no gas flow into the ion source . When the ion source is operating, the pressures are about 1 x 10 -4 and 1 x 10 -5 mbar at the entrance and exit of the ion guide, respectively.
Standard power supplies and amperemeters are used for biasing electrodes and measuring beam currents . 3. Equation of motion A solution of the Laplace equation inside the twowire electrode structure of the ion guide leads to the potential O(r, z) =
(Qa)
V1o (Q ) cos(Qz),
(1)
where a is the aperture radius of the structure, 2%/Q is the electrical periodicity length A, which is twice the distance of two adjacent wires, and V is the applied voltage. An azimuthal dependence can be ignored because of the large value of Qa(= 9.4) . The potentials decrease exponentially towards zero from their boundary values which lie between + V and - V, depending on z. For an ion with a kinetic energy of qU, the equation of motion in the paraxial approximation [2] is d2r = - _V _d Io(Qr) cos(Qz) . 2U dr lo(Qa) dz2 Such an equation cannot be solved analytically. However, the equation can be simplified with the Smooth Approximation [3] by eliminating an oscillatory contribution. The basic idea of the Smooth Approximation is that the solution has a major, slowly varying contribution superimposed by a small, rapidly varying component. For linear differential equations it is shown in ref .
Fig. 1 . Sketch of the testing facility consisting of a multi-aperture source, a 1 an long flexible ion guide, two turbo molecular vacuum pumps, and two Faraday cups for measuring the ion currents before and after the ion guide. The electrical supply consists of : the cathode current I, the discharge voltage Uo, the ion beam voltage U, the accelerator voltage at the second 10 mm diameter grid UA, the current through the neutralizer filament IN , the neutralizer emission current IN., the voltage at the electron suppressor electrode of the first Faraday cup U1, the ion beam current at the entrance of the ion guide I,, the voltages applied to the two ion guide electrodes + V and - V, the voltage at the electron suppressor electrode of the second Faraday cup U,,, and the ion beam current at the end of the ion guide 12. p, and p2 are vacuum pressure meters . Different beam exit directions (3 up to 30 ° can be adjusted by bending the guide hose to curvature radii of 2 m.
J. Schelten, A. Van der Hart / Properties and limitations of an ion guide [3] how the smooth contribution is calculated . For the
nonlinear differential equation (2) one can follow that recipe. In this approximation the equation of motion for the smoothed coordinate is V 21 + d d22 dr (2U) 4 dz
lo(Qr) lo(Qa )
)2
_ 0.
A first integral of this differential equation can be calculated by multiplying eq. (3) with r'. This leads to the critical glancing angle by considering a ray which starts at rt = 0 with the direction rl = ac and is reflected at the boundary, i.e. r2 = a and r2 = 0. The critical-angle relation is
According to eq. (3) the ions move in an effective potential which is almost zero inside the structure and which strongly increases in the vicinity of the boundary. The exponential increase is with an 1/e length of A/4% = 0.5 mm. The height of the effective potential at the boundary is small: Oeff
2
2 _ 1 V
U =aC-8U2)
For U =1000 V and an electrode potential V of 250 V, the effective potential is about 0.8% of the kinetic energy of the ions. It is interesting to compare this effective potential height of an ion guide with the potential barrier heights of light and neutron guides. For Ni-coated-glass neutron guides the potential
47
height is 0.2 t.eV [4), independent of the kinetic energy of the neutrons. For subthermal neutrons of 6.28 A wavelength the relative potential barrier height is only 1 x 10 -4 and even smaller for thermal neutrons. In light guides the abrupt change of the refractive index is wavelength-dependent. If one assumes a 5% refractive-index change in glass fibers one calculates a relative potential barrier height of 1 x 10'1. Thus, the value of 1 x 10 -2 for the ion guide lies between the values of 1 x 10 -4 and 1 x 10' for neutron and light guides, respectively. The equation of motion has been solved numerically. The results confirm the basic idea of the Smooth Approximation that the solution has a small oscillatory contribution superimposed on a smooth trajectory. For beam directions with a < a, and a > ac the probability of reflection closely approaches 1 and 0, respectively. For electrode voltages V larger than U/2 the critical angle does not increase any more with increasing electrode voltage, in contrast to the result of eq. (4) obtained from the Smooth Approximation . A further confirmation of the described motion is obtained from a mechanical model. The profile of the runway represents the r- and z-dependence of the potential as defined in eq. (1) . The sphere model of fig. 2 was constructed with a programmable NC milling machine . For the runway the parameter Qa is 5 instead of 9 .4, which is the value of the ion guide. Nevertheless, one observes reflections of rolling spheres on their slightly oscillating paths. Depending on the glancing angle the sphere is reflected or kicked out of the runway.
sphere. The Fig. 2. Three-dimensional view of the mechanical model with lines emphasizing the profile, and a typical trace of a rolling dimensions are a = 5 cm, A = 6.28 cm and dh = 5 mm . The total length is 0.5 m.
J. Schelten, A. Van der hart l Properties and limitations of an ion guide
48
4. Space charge defocusing In a mean-field approxirnation the Coulomb interaction is described by a beam potential ~ b which is a solution of the Poisson equation:
where p is the charge density of the beam and EO the dielectric constant. Assuming a uniform charge distribution, i.e. a uniform current density at all locations within the guide, the radial dependence of , the beam potential is a parabolic function with its maximum at the beam center. The beam potential can be expressed by 2
~b(r) = D~b 1 - ~ u )
,
(7)
It depends on the beam current I, the kinetic energy qU of the ions, the ion mass M and the relative coordinate r/a . Zo = 377 SZ is the free-space impedance and c the velocity of light . The beam potential drop Orb from center to edge is about 8 V for 1 keV Ar + beam of 60 ~,A . Its relative value is ®~bjU= 0.8 x 10 -Z, identical with the height of the effective potential barrier caused by the electrode structure with an alternating bias of t 250 V. The beam potential lea~3s to a Lnear repulsive force which counteracts the attractive forces caused by the effective potential of the guide. The equation of motion due to both forces is d2r _d _V 2 1 lô(Qr) _ O~b r2 2U a2 dz2 + dr ( 2U ) 4 Î2o( Qa )
From numerical results it has been determined that the voltage V at the guide electrodes should not exceed U/2. With voltages V beyond this limit the amplitude of the oscillatory part of the ion trajectories increases drastically and leads to particle losses. Thus the first term in eq. (10) may be considered ~s being independent of the ion energy qU, provided the electrode voltage can always be set to the same fraction of U. The second term of eq. (10) depends on the mass, energy and current of the ion beam. According to eq. (8) ~~b
a IMt~2Ü-3~2, U i.e. fir 100 times more energetic beams 1000 times more intense beards cans tae guided . rinaiiy, if one is able to compensate the positive charge of the ion beam with thermal electrons either supplied by a hot cathode in the extracted beam or by ionization processes of the ion beam, the repulsive term in eq. (10) is decreased by tkie degree of charge compensation. 5. Experimental results and discussion By measuring the ion beam currents with the second Faraday cup at the end of the straight ion guide for the two ~,ases that the electrodes are grounded and that a voltage of f 250 V is applied to the ion guide electrodes, the transport of ions through the structure is demonstrated . In fig . 3 the guide transmission is plotted versus the ion beam current which enters the ion guide. Ratios of up to 500 have been measured since for
(9)
500 ~
Its first integral determines a new critical glancing angle by again considering a ray which starts at r1 = 0 and ri = a~ and is reflected just at the bounda_a; with r2 f rz and r2 = D. The result is
400 _
1 V 2 z a~ _ ~ ~_~~ ~ m~ -
= 0.
®~b
r~
F_q . (10) has a judicious explanation since a~ is the difference of the relative heights of the attractive and repulsive potentials. There is no reflection if the repulsive interaction exceeds the attractive interaction . The critical glancing angle becomes zero if both interactions are balanced. In general, the space charge term diminishes the critical angle. Zhe discussion of space charge in ion guides is continued with a scaling argument on ion energy and ion current .
300-1 zoo
100 0
T T t 80 100
I~ (uA) Fig. 3. Ratio of the currents Iz at the end of the straight ion guide with and without applied voltages of f 250 V at the guide electrodes versus the ion current h at the entrance of the ion guide. (IN~ = 0, U, _ -100 V and U =1 kV.)
J. Schelten, A. Van der Hart / Properties and limitations ofan ion guide grounded electrodes the current 12 becomes independent of the input current II due to space charge effects, while 12 increases with increasing I, if ±250 V are applied to the electrodes . The very small transmitted current at zero electrode voltages is a consequence of beam divergence and space charge defocussing forces acting in the long and narrow tube of 1 m length and 18 mm diameter. The dependence of the ion beam current at the end of the straight ion guide on the applied voltage at the guide electrodes as shown in fig. 4 behaves qualitatively as one would expect. With increasing voltage the current rises to a saturation value and decreases if the voltage is further increased. This behaviour reflects the increase of of the the ..rcritical. ax agle of reflection with increasing voltage and the particle loss at large applied voltages. In fig. 5 it is shown that an ion beam is transported through bent guides . The amount of bending of the 1 m long ion guide is determined by the angle of beam deflection. At zero applied voltage the ion beam current at the end of the bent ion guide is zero and raises to a saturation value with increasing applied voltage. The more the guide is bent, the more voltage is needed for guiding the beam. This result is again qualitatively in agreement with the critical angle dependence of eq. (4).
49
10 987654 3 1 0 Fig. 5. Ion current 12 at the end of the ion guide versus the applied voltage at the ion guide electrodes. Parameter of the curves is the curvature of the ion guide hose, indicated by the beam exit direction angle ß. (1, = 30 pA, INe =10 mA, U1 -100 V, U =1 kV.)
9-
However, the quantitative analysis of these results will indicate that the ion guide is far from ideal . A guide is called ideal if all. rays with glancing angles less than a critical angle are being reflected and transported through a guide of any length . Light and neutron guides are almost ideal. The ion guide behaves non-ideally because of attenuation, fringing field effects, space charge and lack of charge neutralization.
8-
5.1 . Attenuation
7-
Various collision processes can occur between the 1 keV Ar ions and the Ar gas atoms during the 1 m long flight path in the ion guide . Ion momentum and energy are changed in elastic collisions, while in inelastic collisions mainly the ion energy changes. In such processes the gas atoms become excited or even ionized, or a charge transfer takes place [5] . In those experiments the most probably process is the one of charge transfer where an energetic atom and a thermal ion are generated. For the beam current measurements at the end of the ion guide the process appears as attenuation of the beam. The attenuation factor is
12
0'-* 11 =100pA
11 10-
65-
41
x~x-x-x_I, ~x-x_x `x
3-
=10 uA
x1
2 1
x/~
0
100
200 300 400 500 V± (VI Fig. 4. Ion current 12 at the end of the straight ion guide versus the applied voltage at the guide electrodes . Parameter of the curves is the entrance current fI . U Ne = 0, SI1 = --100 V and U ='1 kV.)
pl (12) ( pl)o where the pressure- path-length product( pl )o for charge -a transfer of 1 keV Ar ions with Ar atoms is 2.0 x 1V -a mbar m [1]. This means that at a pressure of 1.4 x 10 T = exp -
50
J. Schelten, A . Van der Hart / Properties and limitations of an ion guide are large enough in order that the ion ray overcomes the small effective attractive potential from the alternating fields inside the guide, i.e. the deflected rays get lost. A solution to this problem would be an adiabatic onset of the guide fields. This can be achieved by slowly increasing the electrode voltage over quite a number of windings . Another more practical measure would be to shape the guide conically at both ends. For the testing experiments the aperture of the suppressor electrode in front
Fig. 6 . Semi-log plot of the ion beam current 12 at the end of the straight ion guide versus pressure pl in front of the ion guide. At the usual working condition marked by the arrow, the attenuation due to atomic charge transfer is 5056 . (11= 50 IL A, IN. = 0, U1 = -100 V, U =1 kV .)
of the guide was narrowed in order that only ions which are close to the guide axis (r :5 a/2) can enter the guide. At the other end of the guide the Faraday cup was placed very close to the guide exit in order that also ions deflected by the exit fringing fields can reach the second Faraday cup. By this measure the current ratio 12/11 was doubled and the experimental results became interpretable. 5.3. Space charge
mbar in the 1 m long guide the ion beam is attenuated by a factor of 0 .5 . The beam attenuation is experimentally verified by measuring the beam current 12 as a function of the gas pressure pt at the entrance of the guide. Typical results are shown in fig. 6 . The straight line is the log-lin plot corresponding to a (p1 1 )o value of 3 .5 x 10 -4 mbarm. Since the pressure pt is larger than p2 and the pressure inside the guide due to gas flow from. the ion source, this result is in close agreement with the well-known pressure-path-length product (pl )o of 2 .0 x 10 -4 mbar m . However, more important than this agreement is that one gets the attenuation factor under operation conditions, which usually was at a pressure pt marked by the arrow in fig . 6. At this pressure the measured attenuation factor is 0.5 . Its value hardly changes by increasing the ion current fed into the ion guide, by biasing the guide electrodes, or by neutralizing the beam . For a quantitative evaluation of the ion guide this attenuation factor was taken into account .
For the simplest space charge model, based on a constant charge density across and along the guide, a critical angle of reflection, ac was calculated in section 4. According to this model, a,2 varies linearly with the transported current. For a given ion energy, ion mass and electrode voltage V it holds c apt% 2 = a (0) 2 1 - 1s
13)
,
where 1t is the transported current and aß (0) is the a, of eq. (4) . The critical angle vanishes if the maximum current Im is reached .
0,a-
5.2. Fringing field effects In the theoretical section, infinitely long ion guides were treated. lil:aL the Lbeath experiments a ï m long ion guide is tested which has an entrance and an exit . Preliminary experiments have shown that a large fraction of the beam entering the guide gets lost . This loss is caused by the field of the potentials of the outer two half windings . The field expands into the entrance region and is much larger than the field inside the guide. The fringing fields are strongest at a distance r = a from the axis . As a consequence, the entering beam is deflected by this field and in particular that part of the beam which is away from the axis. The deflection angles
0,2
20
40
60
80
100
Fig . 7. Ion current 12 at the end of the straight ion guide with a voltage of t 250 V applied to the guide electrodes versus the entrance ion current h . The current 12 is normalized to T times 11 , where T is the attenuation factor due to atomic charge transfer. The solid curve is a model function with one adjusted parameter. (IN, = 0 mA, U1 = -100 V, U =1 kV.)
J. Schelten, A. Van der Hart / Properties and limitations of an ion guide
The current fed into this solid angle aj It )2 is a fraction of the entrance current : ( 2 I,== I1 Min~ 1, (14)
12
aD )
10
D
where a D is the divergence of the beam at the entrance of the guide . By inserting eq. (13) into eq. (14) one obtains jl
= Min 1,
[I
+
a
a
2 -1
51
a ôV
V* = 0 6
(15)
If one identifies the transported current with I2 /T, which is the attenuation-corrected current at the end of the ion guide, sets Im = 60 pA according to the values of section 4 for an electrode voltage of ±250 V, and assumes aD/a.(0) = 0.9, one obtains the curve in fig. 7 which in general describes the Il dependence of the measured data. One should not expect a better agreement because of the simplifications made in the model. Note for instance, that the current decreases by an order of magnitude along the guide in the experiment while the model assumes a transported current which stays constant along the guide . Nevertheless, the experimental data clearly demonstrate that the space charge of the ion beam is responsible for the small fraction of input current which can be transported by the ion guide. 5.4. Neutralization
If enough electrons are generated by the heated neutralizer filament in the extracted ion beam, the beam becomes at least partly neutralized. As a consequence, the repulsive term in eq. (10) is diminished. Inside the guide the thermal electrons see the strong, exponentially decaying field with inward and outward radial directions depending on position z. Although the fields are strong only near the boundary and almost zero near the axis, the experimental result of fig. 8 seems to indicate that all electrons are pulled out of the ion guide. This suggestion is qualitatively confirmed by the observed current at the positively biased electrode. When a voltage of f 260 V is applied to the electrodes, the current 12 is not influenced by the electron supply as indicated " e .t_ __ L_ s_-___ r_" _ by the lower curve min llg. C. FlUWGVGr, 11 Llle G1e%:Ll VUVJ are grounded and electrons are supplied, the ion beam remains partly charge-neutralized on its way to the second Faraday cup since the current 12 rises by a factor between 5 and 12 according to the upper curve of fig . 8. A quantitative analysis of the currents h atid 12 demonstrates that the larger the entrance current, the less the beam is charge-neutralized .
2
V. - 260V o-o--~-o-o- 0-o_o o-o--.o 1 100
Fig. 8. Ratio of ion currents at the end of the staight ion guide versus the entrance current 11 . Parameter is the applied electrode voltage . I"P and I2°°°'P are the currents with an abundance of charge-neutralizing electrons (IN, =10 MA, U1 = 0 V) and without an electron supply (INe = 0, U1 = -100 V), respectively.
In summary it can be stated that for 1 keV Ar ion beams the ion guide is far from ideal, mainly because of repulsive space-charge forces. Thermal electrons provided to charge-neutralize the beam are withdrawn in the ion guide. Acknowledgements We are grateful to U. Kurz and W. Reimer for designing the test facility and to J. Zillikens for the construction of the flexible ion guide and the assembly of the test facility, and for his assistance during the measurements. We thank Dr. R. Lehmann and Dr. M. Pabst for stimulating discussions. References Ion-Source Operation (Commonwealth Scientific Corporation, 1984). P. Grivet, Electron Optics (Pergamon, 1972) p. 95 ff. H. Bruck, Accélérateurs Circulaires de Particules, Chap. IX (Presses Universitaires de France, 1966). B. Alefeld, J. Christ, D. Kukla, R. Scherm and W. Schmatz, JÜL 294-NP (1965) . H. Neuert, Atomare Stossprozesse (Teubner Studienbücher, Physik. 1984).
[il H.R_ Kaufman_ Fundamentals of
[2] [3 1, [4] [5]