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magnetic fields play a double role in the cosmos : first , planetary , stellar , and galactic fields are produced by the homogeneous dynamo effect in moving electrically conducting fluids .
second , magnetic fields can accelerate tremendously the formation of stars and black holes by enabling outward directed transport of angular momentum in accretion disks by virtue of the so - called magnetorotational instability ( mri ) .
this instability was discovered as early as 1959 , when velikhov showed that a taylor - couette flow in its hydrodynamically stable regime ( i.e. with outward increasing angular momentum ) can be destabilized by an applied axial magnetic field @xcite .
it was only in 1991 , however , that the importance of mri for accretion disks in the vicinity of young stars and black holes was realized in a seminal paper by balbus and hawley @xcite .
the last decades have seen tremendous theoretical and computational progress in understanding the dynamo effect and the mri .
the hydromagnetic dynamo effect has even been verified experimentally in large - scale liquid sodium facilities in riga , karlsruhe , and cadarache , and is presently studied in laboratories around the world @xcite .
in contrast , attempts to study the mri in the laboratory have been less successful so far .
recently , an mri - like instability has been observed on the background of a turbulent spherical couette flow @xcite , but the genuine idea that mri would destabilize a hydrodynamically stable flow was not realized in this experiment .
one of the basic problems for the experimental investigation of the  standard mri 
, with only an axial magnetic field being externally applied , is the need for flows with large magnetic reynolds numbers @xmath0 .
the crucial point is that the azimuthal field , which is essential for the mri mechanism to work , must be produced from the applied axial field by induction effects proportional to @xmath0 .
the natural question , why not substitute the induction process by externally applying the azimuthal field as well , was addressed by hollerbach and rdiger @xcite . exemplified in a taylor - couette configuration
, it was shown that the scaling properties for this  helical mri  , as we call it now , are completely different from those of the  standard mri  . while the latter is governed by the magnetic reynolds number @xmath0 and the lundquist number @xmath1 ,
the former depends only on the hydrodynamic reynolds number @xmath2 and on the hartmann number @xmath3 . for liquid metals , with their small magnetic prandtl number @xmath4
, this makes a dramatic difference for the feasibility of mri experiments , since @xmath5 and @xmath6 .
=    we have to point out , though , that there is no real breach between  standard mri " and  helical mri " .
this can be clearly seen in fig . 1 of @xcite , where the critical @xmath0 is plotted against the rotation ratio @xmath7 of outer to inner cylinder of a taylor - couette set - up . the extremely steep increase of this curve at the rayleigh line , which occurs for a purely axial magnetic field , is just smeared out when an azimuthal field is added .
in this paper , we summarize the main results of a first experimental verification of this idea obtained in the framework of the promise experiment ( potsdam rossendorf magnetic instability experiment ) which were already published in @xcite , and we report some new results of an improved version of this experiment .
the basic part of promise is a cylindrical containment vessel v made of copper ( see fig .
the inner wall of the vessel v is 10 mm thick , and extends in radius from 22 to 32 mm ; the outer wall is 15 mm thick , extending from 80 to 95 mm .
this vessel is filled with the eutectic alloy ga@xmath8in@xmath9sn@xmath10 which is liquid at room temperatures .
the vessel v , which is completely made of copper in the first version of the experiment ( henceforth called promise 1 ) , is fixed , via an aluminum spacer d , on a precision turntable t ; the outer copper cylinder of the vessel represents the outer cylinder of the taylor - couette cell . the inner copper cylinder
i of the taylor - couette flow is fixed to an upper turntable , and is immersed into the liquid metal from above .
it has a thickness of 4 mm , extending in radius from 36 to 40 mm , thus leaving a gap of 4 mm between this immersed cylinder i and the inner wall of the containment vessel v. the actual taylor - couette cell extends in radial direction over a cylindrical gap of width @xmath11 mm , and in axial direction over the liquid metal height @xmath12 mm , resulting in an aspect ratio of 10 .
= hz ( i.e. @xmath13 ) , @xmath14 ( i.e. @xmath15 ) , @xmath16 a ( i.e. ha=7.9 ) .
( b ) promise 1 with @xmath17 a ( i.e. @xmath18 ) .
( c ) promise 2 with @xmath19 a ( i.e. @xmath20).,title="fig:",scaledwidth=95.0% ]    in the promise 1 configuration , the upper endplate is a non - rotating plexiglass lid p fixed to the frame f. the bottom , however , is simply part of the copper vessel v , and rotates with the outer cylinder . with respect to both their rotation rates and electrical conductivities ,
there is thus a clear asymmetry in the end caps .
figure 2a shows the changes made for promise 2 to improve this situation : first , both end caps are made of insulating material in order to avoid short - circuiting of currents along the copper end cap at the bottom ( those currents had been shown to be dangerous by possibly changing the rotation profile via azimuthal forces @xcite ) .
second , both the upper and the lower end caps are split into two rings , the inner rotating with the inner cylinder and the outer rotating with the outer cylinder . in @xcite
it had been shown that this splitting yields a minimization of the ekman pumping if the position of the splitting is at 0.4 of the gap width @xmath21 .
third , the co - rotation of the two rings with one of the cylinders made it necessary to change the signal path of the ultrasonic transducers .
these two transducers provide full profiles of the axial velocity along the beam - lines parallel to the axis of rotation .
while in promise 1 they are inserted in the upper plexiglass end cap that is fixed to the laboratory frame , in promise 2 they must be connected via a sliding contact to the signal processing computer ( dop 2000 ) .
the configuration of magnetic fields is the same for promise 1 and promise 2 .
an axial magnetic field in the order of 10 mt is produced by a double - layer coil with 76 windings ( c in fig .
the omission of windings at two symmetric positions close to mid - height , as seen in fig .
1a , was motivated by a coil optimization to maximize the homogeneity of the axial field throughout the fluid volume .
the coil is fed by currents up to 200 a , beyond which a significant heating of the coil sets in . the azimuthal field , also in the order of 10 mt , is generated by a current through a water - cooled copper rod r of radius 15 mm . the special power supply ( ps in fig .
1c ) for this axial current is capable of delivering up to 8000 a.
we have carried out a large number of experimental runs in order to cover a wide range of parameter dependencies . typically , the duration of an experimental run was 1900 sec , after a waiting time of one hour and more .
many details for the promise 1 set - up can be found in the publications @xcite .
= 0.245 , 0.255 , 0.265 , and 0.275 , at @xmath22 hz , @xmath23 a , @xmath24a . ,
title="fig:",scaledwidth=95.0% ]    = hz , @xmath23 a , and two values of @xmath24 a and 7000 a , which corresponds to @xmath25 and @xmath26 respectively .
the experimental values ( full lines ) are compared with the numerical results of a 2d solver , and with the results for the absolute and the convective instability of a 1d solver ( courtesy of jnis priede).,title="fig:",scaledwidth=95.0% ]    one of the most significant features of the mri is that , for fixed @xmath2 and fixed azimuthal field @xmath27 , it shows up only in a finite interval of the hartmann number @xmath28 ( @xmath29 is the conductivity of the liquid , @xmath30 its density , and @xmath31 its kinematic viscosity ) .
this appearance and disappearance of a travelling mode is a suitable indicator for the existence of the proper mri mode and its distinction from other possible flow structures .    in fig .
2b , c we represent the results for rotation rates of @xmath32 hz ( i.e. @xmath13 ) and @xmath14 ( i.e. @xmath15 ) which is slightly above the rayleigh value @xmath33 . the current in the coil was fixed to @xmath16a ( i.e. ha=7.9 ) . in the promise 1 case ( fig .
2b ) , the axial current was set to @xmath17 a ( i.e. @xmath34 ) , in the promise 2 ( fig .
2c ) case to @xmath19 a ( i.e. @xmath20 ) , a difference that is , however , not essential .
the grey scale of the plots indicates the axial velocity component @xmath35 measured along the ultrasound beam , from which we have subtracted the ( z - dependent ) time average in order to filter out the two ekman vortices which appear already without any magnetic field .
these ekman vortices , which in the promise 1 version are characterized by inward radial flows close to the upper and lower end - plates and a jet - like radial outflow in the centre of the cylinder @xcite , are significantly suppressed in the promise 2 version due to the use of split end caps . in promise 1 ,
the wave dies away at the position of the radial jet ( which is not always at mid - height ) .
in contrast to this , in promise 2 the wave propagates throughout the total height of the cell .
this much improved behaviour of the mri in promise 2 can be visualized nicely when crossing the rayleigh line .
it is known @xcite that the travelling wave appears already with a stationary outer cylinder , i.e. at @xmath36 , although with a very low frequency . with increasing @xmath37 , the wave frequency increases and typically reaches a value of @xmath38 at the rayleigh value @xmath39 .
figure 3 shows now in detail what happens with the travelling mri wave when @xmath37 crosses the rayleigh line .
the parameters for this run were @xmath22 hz ( i.e. @xmath40 ) , @xmath23 a ( i.e. @xmath41 ) , @xmath24 a. it is clearly visible that the mri wave is still present at @xmath42 , becomes significantly weaker at @xmath43 , and has completely died at @xmath44 .
this transition is further analyzed in fig .
4 which shows the rms of the axial velocity perturbation in dependence on @xmath37 , now both for @xmath24 a and @xmath19 a ( which corresponds to @xmath25 and 4.5 , respectively ) .    the measured values ( full lines )
are compared with the numerical results of a 2d solver ( dashed lines ) , but also with the results of a 1d solver for the onset of the absolute and the convective instability @xcite ( courtesy of jnis priede ) .
it is most remarkable that the 1d results for the onset of the absolute instability correspond nearly perfectly with the results of the 2d solver , while the thresholds for the convective instability are situated at much higher values of @xmath37 .
compared to the 2d numerical curves , the experimental curves are shifted only slightly towards higher @xmath37 . as expected , we see also that for increasing @xmath45 the threshold of the instability shifts to higher values of @xmath37 .
we have obtained experimental evidence for the existence of the mri in current - free helical magnetic fields .
the symmetrization of the axial boundary conditions and the use of split end caps in promise 2 has led to a strong reduction of the ekman pumping and hence to an avoidance of artefacts in the radial jet flow region .
the mri wave extends clearly beyond the rayleigh line , and its behaviour is in good correspondence with both 2d simulations and 1d simulations for the absolute instability , but in stark contrast with 1d simulations for the convective instability .
this indicates that the observed mri wave is indeed a global instability and not only a noise triggered convective instability as claimed recently @xcite .
further dependencies of the mri on parameters like @xmath2 , @xmath45 , and @xmath3 , as well as their comparison with numerical predictions will be published elsewhere .
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the magnetorotational instability ( mri ) plays an essential role in the formation of stars and black holes . by destabilizing hydrodynamically stable keplerian flows , the mri triggers turbulence and enables outward transport of angular momentum in accretion discs . 
 we present the results of a liquid metal taylor - couette experiment under the influence of helical magnetic fields that show typical features of mri at reynolds numbers of the order 1000 and hartmann numbers of the order 10 . 
 particular focus is laid on an improved experiment in which split end caps are used to minimize the ekman pumping .