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an increasing interest in short x - ray pulses requires short electron bunches in storage rings . over the years
, the traditional way to get short bunches is to decrease the momentum compaction factor by low-@xmath0 optics @xcite .
however , the average current per bunch will decrease to the order of @xmath1a magnitude with low-@xmath0 , limited by beam instability and microbunching due to coherent synchrotron radiation and other collective effects @xcite .
bessy ii presented an idea to produce long and short bunches alternatively in their storage ring : with two superconducting cavities , 3rd harmonic and 3.5th harmonic of the fundamental rf cavity , the voltage gradient produced by two sc - cavities could add up at even points for bunches focusing to get short bunches , and cancel each other at odd points to get long bunches @xcite .
the new method greatly improved the capacity of storing current in the ring .
nonetheless , bessy ii is filled with 400 buckets , which is the multiples of 2 , leading to the result of choose the second sc - cavity as a 1/2 times higher harmonic one .
what if the ring is with odd buckets , such as multiples of 3 , 5 , 7 ? in this paper , we find the problem could be solved by choosing the frequency of the second sc - cavity ( sub harmonic cavity ) in a different way .
for a ring , whose minimum common factor is @xmath2 ( @xmath3 ) , the frequency of the sub harmonic cavity could be chosen @xmath4 times higher than harmonic one .
several typical situations are listed in table.[tab : cavity harmonic number ] , in which @xmath5 is chosen accord to the voltage and frequency of original cavity in different rings .
.[tab : cavity harmonic number]harmonic number with different buckets number [ cols="^,^,^ " , ]
a scheme is presented to operate the hls ii ring with simultaneous medium , long and short bunches .
the short bunches current limit can be increased more than 60 times compared to low-@xmath0 mode .
the frequencies of two superconducting cavities are both near 1.3 ghz , which are easy to achieve by tuning , for 1.3 ghz is a common frequency for sc - cavities @xcite . and the voltages are about 2 mv , which is easy to be realized by single - cell or two - cell structure , so the hom problems will be simplified .
we thank a. chao and j. wu for useful discussions and encouragements . this work was supported by national natural science foundation of china under contract no.11327902 ,
no.11175180 , no.11175182 and u.s .
doe under contract no.de-ac02-76sf00515 .
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a scheme with two superconducting rf cavities ( sc - cavities ) is designed to upgrade electron storage rings with odd buckets into multi - length bunches . in this paper , 
 hefei light source ii ( hls ii ) is given as an example for odd buckets . in accordance with 45 buckets , which is multiples of 3 , 
 three different length of bunches generated simultaneously is proposed in the presently applied user optics . 
 the final result is to , without low-@xmath0 optics , fill hls ii with long bunches of 50 ps length , medium bunches of 23 ps and short bunches of 6 ps . 
 each third buckets can be filled with short bunches , of which the current limit is up to 6.6 ma , more than 60 times the value of low-@xmath0 mode . 
 moreover , particles tracking about beam dynamics performed by elegant and calculations about beam instabilities are presented in this paper .    
 multi - length , odd buckets , superconducting cavities , hls