Summary of Experimental Results in LHD
Since the successful production of the first plasma in 1998．outstanding plasma parameters have been achieved．The electron and ion temperatures of 10 keV, plasma stored energy of 1.3 MJ have been recorded independently during 6 year operation in LHD．These results show that LHD has plasma confinement proper ties comparable to those of the world's largest fusion machines．
Attained Plasma Parameters
Beta value is the figure of merit which indicates the efficien cy of the plasma confinement．It is defined as the ratio of the plasma pressure to the magnetic Pressure．Economical magnetic fusion confinement devices are required to achieve a beta value of more than 5％．The figure on the right shows the recorded beta values in world wide helical plasma confinement devices．The beta value in LHD extends year by year and it is now a world record．
The pressure of the plasma is proportional to the cross pro duct of density and temperaute. lt is well known that the plasma excites instabilities leading to escape across the con fining magnetic field, when the pressure exceeds a critical value．Recent experimental results might indicate the possi ble avoidance of deleterious instabilities in achieving a high beta value．Figures on the right show the wave forms of a typical high beta shot. The most unfavorable m=1/n=1 mode appears around the time when the beta value exceeds 3%, but is almost suppressed after 1 s as the beta value continues to increase up to 4%．An m=2/n=3 mode which is supposed to be excited in a more outer region than that of the n=1/m=1 mode stays but does not seem to affect the beta value．An m=2/n=1 mode which is excited near the plasma center and had been at tne low beta（less than 2.5％）does not appear． These results infer the presence of some mechanisms of self organization or instability suppression.lt is a challenge to explore a new framework of theoretical study in this field. Furthermore．it can stimulate a reconsideration of the theo retical beta limit of helical fusion devices and can give a bet ter future prospect of a fusion reactor. The figure on the left shows the progress of several import ant plasma parameters, electron and ion temperatures and plasma duration time by experimental campaign. Each experimental campalgn of about a half of a year was performed once a year except the first and second cam palgns in 1998.
Recent Results of Theory and Computer Simulation Researches
A new super computer system has been introduced since 2003 （main memories;1.3tera Bytes, calculation speed;1.41tera Flops） and is now in full operation pro ducing new knowledge and information on fusion plasmas and complexity science．Fur ther,remarkable progress has been made in computational techniques and related utilites． The new system achieved a world record in calculation effi ciency．