JAERI-Conf 95-021

PD-01
NEXT-STEP ECRIS AND 2m LENGTH 4.52 GeV ADVANCED ACCELERATOR:
Novel Extraction of Trapped Ions and their Acceleration-Final Focusing
by Nonneutral and Neutral Plasmas
Masanobu NIIMURA, Takahide NAKAGAWA, Akira GOTO, and Yasushige YANOThe Institute of Physical and Chemical Research (RIKEN), Wako City, Saitama 351-01 Japan
Abstract For more efficient extraction of high-charge
state (HCS) ion beams and for much shorter pulse beam
production than presently achievable, we propose a pulsed,electric (E-) field to be induced inside an ECR ion source.
Advantages over conventional upgrading technologies,
right range of the E-field intensity, and low-emittance
extraction hardware are described. It is shown that the Efield method can extract only HCS ions with a drasticallyhigh upgrading factor surpassing the e-beam method,
without disturbing the rf-heated hot electrons inside ECRellipse. Further, in order to accelerate heavy ion beams toa GeV/u energy (case: U238, Z=60) and to focus it to a
submillimeter beam size we present preliminary studies
on a high-acceleration gradient (9Ge V/m peak) nonneutral
plasma accelerator and a neutral plasma final beamfocuser, respectively. A novel 4.52GeV accelerator
coupled with a neutralizing and focusing z-pinch plasma
seems feasible in an elliptical chamber of 2m length.
1. Introduction
The ECR ion source (ECRIS) has readily established
its position as the l11ost efficient HCS ions injector forheavy ion linacs and cyclotrons. This paper searches a wayof further improvement of the performance not only in
CW but also pulsed operations, so that it can evolve
useful source for also synchrotrons. The work is based on
our recent discovery of the physical scenario for upgrading
the extraction efficiency of HCS ion beams in ECRIS 1),
the concept of which prompt us to design not only thenext-step ECRIS but also an advanced accelerator.
As a positive use of the space-charge potential has let
ECRIS grow as the best HCS ions injector, this paper
suggests deepening and tailoring of the space-chargepotential for accelerator applications. Concept of theheavy ion plasma accelerator (HIPAC) can be found in theliterature2) and the experiments have been performed since1970's. A radial potential difference of 300 kV waspractically measured3) inside a toroidal chamber, whose
minor radius a=8cm, by filling it with electrons at thedensity ne=I010 cm-3. Electrons are no need to be hot forthe potential formation as long as they are confined in achamber during the ion acceleration. They all used atoroidal chamber for acceleration and trapping of ionsinside a topologically closed potential-well which can beformed with magnetically confined electrons. This paper
describes a novel extraction and focusing of acceleratedbeams, which is impossible with a toroidal chamber but
possible with an elliptical one.

2. Review of Upg1·ading Physics
The HCS ion beam current from an ECRIS is known
to enhance significantly by employing so-called upgrade
technologies such as (i) electron (e-) beam injection, (ii)wall-coating, and (iii) gas-mixing. The upgrading factor, 11
defined by the ratio of extracted ion beam-current 'with' to'without' an upgrade technology increases sharply together
with charge-state, Z. The physical scenario of upgradingmechanism was discovered based on the experimentallyand numerically observable facts: (1) Remarkablesimilarity among the effects of (i)-(iii), (2) Experimental
11 that scales by exp Z, but only for the Z's above a
critical one, Z0 ; existence of a potential-well which cantrap the otherwise-lost HCS ions for a time enough forcharge multiplication, (3) Parametric study ofsimultaneous rate-equations has indicated that the charge
state distribution (CSD) may become anomalous,
meaning that the HCS ion density increases with Z, only
if the diffusion loss becomes negligible along with thecharge exchange loss from a given system; existence of anegative potential.
Thus we were forced to draw a conclusion that themajor role of all those upgrading technologies (i) - (iii) is
to help-tapping the HCS ions otherwise-trapped quasiindefinitely inside the potential-well. We have identified
the mechanism to be the local lowering of potential
barrier (LLPB) or bitten dog-food bowl (BDFB), by which
the cw endloss current can locally increase its magnitudein the range of HCS. Here, the terminology of 'endloss'
refers the leakage flown ou.t of potential-end. In 3Dpicture, 'potential-end' corresponds the surface of an ECRellipse. On the other hand, 'local' refers a part of thepotential-end. This paper will show that the LLPB tends
to occur preferentially along the axisymmetric axis of
ECR device even for the cases of (ii) and (iii).

2 .1 Physical P1·oof of Experimental Results
The present day ECRIS's in the CW mode of operation
are all tapping the endloss current, relying on animperfection of the electrostatic confinement. The trappedions at the charge state Z and energy kTiz can leak out ofa potential-well of depth il<l> with probability exp (- Zef.<P/kTiz). Zero probability (f.<!>~ oo, kTiz ~ 0) is ideal for
production of highly HCS ions and low emittance beams,
but such a perfect confinement is not good as an ion
source which should extract the maximum possible ion
beam current, Ib = ZeSprs: 1)·( Zef.<jl)
lb=l0 expkT ,10 =0.61ZeSpvBnz(O)

(l)

IZ

Here, the expression of 10 is obtainable from the flux
conservation, Sendr end =Sprs· The CW endloss current
of Hz ions is Iz = ZeSendr end• where send is the ion
escaping surface at the potential-end. All the loss current,Sendrend was assumed to be extracted eventually via thesheath surface, SP near the plasma electrode located atECRIS exit. r s is the ion flux at the sheath edge andknown to be rs = vBns, where VB= (kT e/mi) 112 is theBohm velocity and the sheath edge density is ns""0.61n 0 .
Here, n 0 is the density of HCS ions of interest in theperipheral plasma, which is assumed uniform with the-466-

JAERI-Conf 95-021
endloss density just leaking out at the potential-end,nz(Lp/2)==nz(O)exp[ -ZeA<j>/ kTiz].
Suppose the bight of A<l> was lowered locally by an ebeam injection to A<!>- A<l>eb• Eq. (1) gives(2)This expression indicates that Ieb should increase as A<l>eb
increases. This is consistent with experimental
observation: the ion (i-) beam current enhanced as the ebeam current was increased. Thus, the e-beam must be
lowering the A<l> or increasing the magnitude of A<l>eb·If we take the ratio of Eq.(2)/Eq.(l) we have
11 == Ieblleb = exp [ZeA<I>eb]
kT- exp [Z]

(3)

1Z

Here we estimate a right range of the E-field intensity
for the novel extraction technology proposed.
3.1.1 Motion of Charged Pat·ticles Inside a
Magnetic Bottle First, we study if the electron cloud
can be contained magnetically even after the application ofan external E-field. Consider an electron gyrating aroundthe axisymmetric B-field which increases slowly parallelto the direction of +z axis. Then, in the cylindrical polar
coordinates, Br is always pointing z-axis. The direction ofgyration is anti-clockwise if seen towards +z axis from theback of the plane which is perpendicular to the z-axis.
_Writing the linear velocity of gyration by v.Le• the v.l.ex
B r is in the negative (or -z) direction. Therefore, theLorentz force can be expressed by F= - e[ vxB] = ev.l.eBr.
Here, Br =- (rL/2) (dBzldz) which is a Maxwell equation,V•B = 0 expres·sed in the axisymmetric system ({)/()9=0),
provided that dBzldz is approximately constant with rover
the distance ofLarmor radius, rLe == v.l.e/roce· Since ffice""'This result agrees well with a number of experimental
results where 11 _ exp [Z] is evident. Since 11 ~ 1 in theregion~ Z 0 , Eq. (3) would be better expressed by

eB/m, the axial motion of electrons can be expressed by[eA<I>eb]ll(Z) = exp L~ (Z- Z0 ) ,nr~it=-e[v.l.exBrJ=-!-leaz•(Z~ Z0 ){4)1Z

Here, Z0 is the threshold with which the confinement time
is long enough for producing HCS ions of interest;kTiz~Z 0 eA<I>eb· Z 0 increases proportionately with theionization time needed for the Z of the atom of interest.

2.2 Wall-Coating and Gas-Mixing to Form ane-Beam Like Electt·on Channel on Axis
The wall-coating works similar way as an e-beam gun.
Secondary electrmis (ne8 ) can be generated when HCS ionsapproach the wall which is coated with low work-function
material like MgO. They are accelerated by the positive
plasma potneital towards the circumference of ECR-zone
and there they tend to stagnate. Those nes pointing theECRIS axis will be 'beamed' along the axis due to joining
with incoming nes together with MMF focusing effect;
the nes is thus at least two-times denser on axis than thecircumference of ECR zone. This is a formation of quasistationary 'e-beam', which can lower A<!> near the axis.
Gas mixing too can behave an 'e-gun' by two steps.
Step 1: Completely stripped ions of the lighter gas suchas 02 and H2, fed either internally from oxidized-wall orexternally by gas-mixing, can cool Tiz of the higher Z
ions as they 'evaporate' out of ECR zone. The lowered Tiz
can guarantee to become highly HCS ions. Such highlyHCS ions_ only can generate a number of nes to exceed theown Z-number as they approach the (oxidized) wall
surface. Step 2: The nes emitted from the wall would
follow the same process as the case of wall-coating.

3. Novel Extraction of Trapped HCS Ions
Conventional technologies (i)-(iii) are a destructive
extraction in terms of the original bight of ECR heatedpotential-well. We search a non-destructive but efficient
way of extraction. The probleni can be solved if only thetrapped ions are accelerated by an axial electric field Ez
inductively induced inside the ECR zone, without loosing
the ECR heated hot electrons from the zone.
3.1 Theory of E-Field Extt·action()Bzdvz

Io!-le""'2mv.l.e-!B (5)This Eq.(5) states that electrons experience a -z directed
force Fz=J-l-e(dBzldz) in the region where dBzldz~O. Fz is
proportional with the electron magnetic moment, J-le, Thismeans that electrons can be safely confined inside a pair of
MMF even after an Ez was applied, if eEz<< !-le (dBzldz).
Since the total kinetic energy W == mv 2/2 == W z + W.1.
is constant (dW/dt=O), Eq. (5) gives the invariance of!-! ordJ-l- /dt =0. The invariance of !-! tells that at the turning
epoint B=BR and W.L=W so that !-le=W/BR. However, BR
should equal BEeR at the ECR surface since there produces·the largest perpendicular energy W,. Should a particle-'--max

move along the B-field line to a location B~BEeR· there
W should be higher than W
from the in variance of
11-'--'-max

J-l-, which is unlikely. If Bm=10kG and B0 =BR in a 10GHz ECRIS (BEeR ""BR =3.57 kG), we have AB/BR =1.80, Az=10 em, and mv/ /2 = 500 eV so that
1oAB
1Ez << 2e mve- BocR Az = 90 V/cm

(6)

is the safe electric field to keep the ECR zone in position.
On the other hand, ions are not difficult to extract froma magnetic bottle since they are usually not well confined
anyway due to the fact that ru /rLe"' (M/m) 112 /Z >1
under Ti=Te unless Z is very large. However, ECRIS ions
are high-Z and kTiz may be very low inside the spacecharge potential of electrons in the steady stqte. This cancreate the situation ru "'rLe· Then, Fz =- Jli (dBz f{)z),
but!-!·""'
Mv--'-1 2 /2B = kT 1·/BEeR- Thus J-l-:<<!-l1
1e , and the1 •condition ZeEz~!-li (dBzldz) determines the minimum Ez:
1o AB
1Ez ~ 2Ze Mv( BECR Az = 0.90 V/cm

(7)Here, mvi 2 /2=50eV and Z=IO was assumed. Right E-fieldshould thus be within the range, 0.90 ~z(V/cm)<<90.

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3.1.2
Motion of Charged Pat·ticles Inside
an Electron Space Chat·ge Potential of ECR
Ellipse Here, we study if heavy ions can indeed heextracted out of an ECR ellipse by applying an electricfield. The original electron space charge potential inside ofECR ellipse is filled by ions but only partially, since theperipheral ions are aheading outward walls from the timeof the formation of potential well. Therefore, the potential
barrier needed to cross for trapped ions is the il<l> generated
by the excess charge density, e(ne- 1:Zznz). In the energy
wise, Zeil<J>;:::kTiz for high-performance ECRIS's andkTiz::;;50eV for typical devices. The e-beam injection atLBL lowered the hight of positive plasma potential VP
which is same to lower il<l> by il<l>eb=10eV to obtain Ll<l>10V. Their experiment can be explained well by the set ofparameters: Z=10, il<l>=20eV~ kTiz=50eV. For this weneed an extra Ez to satisfy ZeEzlp;:::20eV, where lp""5cmis the useful length of acceleration which is one half ofthe length of a typical ECR ellipse. Thus, for Z=lO ions
we need Ez;:::0.4 V/cm. We choose Ez= 4 V/cm whichsatisfies also the above condition 0.90::;;Ez(V/cm)<<90. A
drastic improvement in 11 is evident with the E-field
method. Table I compares the 11 with the e-beam case.
Table I: Improved 11 byE-field methodEz = 4V/cm Z=lO
Z=15n(e-Beam)
11 (E-Fie1d)

7.39
24.5

19.9
169

Fig. 1 shows schematic drawings of the next-step
ECRIS proposed. The emittance is expected good becauseof the use of drift tube with a griddle front and due to thefact that E-field method can extract highly HCS ionswhose Tiz is likely zero4) due to their location ofconfinement close to the bottom of parabolic potential.
~~a~~~~~:mu~

The axis of a cylinder of radius a=1 m filled with 100%
electrons at density ne=I012 cm-3 is holding a negativeelectric potential against grounded wall given byneil<l>= 4 ; 0 a2 = 4.52 x10-9 ne(m-3) a(m)2 = 4.52 GeV(8)Such a charge cylinder conta.ins a huge acceleration
gradient, E 1=9.04GeV/m at the wall, although zero at r=O.
This paper proposes a utilization of such space charge
field for an economical alternative of heavy ion
accelerators. We will use a fat elliptical chamber of length
2m tilled with only electrons. In the both midplanes of its
depth as well as of its length the electric potential
distribution should be similar to the one for Circular crosssection of charge cylinders. If for an example, 238U ionsat Z=60 were injected at one end of the ellipse, they would
attain the energy 1.14 GeV/nucleon at the midplane ofellipse. What is difficult is to extract particles right at thebottom of the potential-well. Our innovative idea ofachieving this is to flatten the potential in the decerelation
section by using a z-pinch plasma. A high energy, focused
beam may be extracted from the other end of ellipse.
Fig.2 shows a z-pinch device to be set along the axis
starting from the midplane. The plasnia will be fired at themoment when a bunch of ions impinged in to the firstelectrode. The metallic gas needed for producing soliddensity plasma will be generated itself from electrodesurfaces when flashes over. Inside the plasma the self
defocusing effect of ion beam can be neutralized and thus
the IxB self-focusing effect may become effective before
reaching the relativistic speed. However, our calculationshows that force density of the self-focusing is muchsmaller than the kinetic pressure of pinch plasma. With
moderate to solid-state z-pinch densities, ne= 1024-1028. m-3 (kT=1 keY), we obtain p= nkT,;1.6x103 -i.6x 107
atm. Sumbillimeter focus size can thus be expected.

-Acclerato<Sectioll----Focusiog Sectioll(a) H...-.....1 PIQaa Ac:cdcntac aad z-Piac.k Pluaa B--. Foe.-.

-L"'•0'•{II) PriJociple a( E-l'ield Eldncliaa a( lou fma Patemai-WeiL(b) P!.naa T.Uoriq Elec:troa S~l" Polelltiai-Prof"ale ld t •to.

~~--~~~--~--~~--~~zlpL

Fig.2. A 2m, 4.25GeV advanced accelerator schematics.

(c) Mapcei"'IIT T....... l l e U I I - •••• if eE. «J. 0 (lB.V o:).

Fig.l. E-field extracting, efficient ECRIS schematics.
4. Nonneutral Plasma Advanced Acceleratot·and Neutral Plasma Beam Focusing

1) M. Niimura, T. Kageyama, T. Nakagawa, A. Goto, and Y.
Yano, Proceedings of ECR-12, INS-J-182. p.141 (1995).
2) G.S. Janes et al., Phys. Rev. 145, 925 (1966).
3) W. Clark et al., Phys. Rev. 37. 592 (1976).
4) A. Irani and N. Rostoker, Particle Ace. 8, 107 (1978).

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