• L. Haenichen, W.F.O. Müller, T. Weiland
  TEMF, TU Darmstadt, Darmstadt
• O. Boine-Frankenheim
  GSI, Darmstadt

Beam cou­pling impedances have been iden­ti­fied as an ap­pro­pri­ate quan­ti­ty to de­scribe col­lec­tive in­sta­bil­i­ties caused through beam-in­duced fields in heavy ion syn­chrotron ac­cel­er­a­tors such as the SIS-18 and the SIS-100 at the GSI fa­cil­i­ty. The impedance con­tri­bu­tions caused by the mul­ti­ple types of beam­line com­po­nents need to be de­ter­mined to serve as input con­di­tion for later sta­bil­i­ty stud­ies. This paper will dis­cuss dif­fer­ent ap­proach­es to cal­cu­late the Cou­pling Impedance con­tri­bu­tion of fer­rite de­vices, ex­ploit­ing the abil­i­ties of both com­mer­cial codes such as CST STU­DIO SUITE® and spe­cif­ic ex­ten­sions of this code to ad­dress kick­er re­lat­ed prob­lems in par­tic­u­lar. Be­fore ad­dress­ing ac­tu­al beam­line de­vices, bench­mark prob­lems with cylin­dri­cal and rect­an­gu­lar ge­om­e­try will be sim­u­lat­ed and the re­sults will be com­pared with the cor­re­spond­ing an­a­lyt­i­cal for­mu­la­tions.

• S. Appel, T. Weiland
  TEMF, TU Darmstadt, Darmstadt
• O. Boine-Frankenheim
  GSI, Darmstadt

For the fu­ture op­er­a­tion as an in­jec­tor for the FAIR pro­ject the SIS18 syn­chrotron has to de­liv­er in­tense and high qual­i­ty ion bunch­es with high rep­e­ti­tion rate. One re­quire­ment is that the ini­tial mo­men­tum spread of the in­ject­ed coast­ing beam should not ex­ceed the limit set by the SIS18 rf buck­et area. Also the Schot­tky spec­trum should be used to rou­tine­ly mea­sure the mo­men­tum spread and rev­o­lu­tion fre­quen­cy di­rect­ly after in­jec­tion. Dur­ing the trans­verse mul­ti-turn in­jec­tion the SIS18 is filled withμbunch­es from the UNI­LAC linac at 36 MHz. For low beam in­ten­si­ties theμbunch­es de­bunch with­in a few turns and form a coast­ing beam with a Gaus­sian-like mo­men­tum spread dis­tri­bu­tion. With in­creas­ing in­ten­si­ty we ob­serve per­sis­tent cur­rent fluc­tu­a­tions and an ac­com­pa­ny­ing pseu­do-Schot­tky spec­trum. We will ex­plain that the mul­ti-stream in­sta­bil­i­ty of theμbunch fil­a­ments is re­spon­si­ble for the tur­bu­lent cur­rent spec­trum that can be ob­served a few 100 turns after in­jec­tion. The cur­rent spec­trum ob­served in the SIS18 and the re­sults from a lon­gi­tu­di­nal sim­u­la­tion code will com­pared to an an­a­lyt­i­cal model of the mul­ti-stream in­sta­bil­i­ty in­duced by the space charge impedance.

• F.B. Petrov, T. Weiland
  TEMF, TU Darmstadt, Darmstadt
• O. Boine-Frankenheim
  GSI, Darmstadt

Elec­tron clouds gen­er­at­ed by resid­u­al gas ion­iza­tion pose a po­ten­tial threat to the sta­bil­i­ty of the cir­cu­lat­ing heavy ion beams in the ex­ist­ing SIS-18 syn­chrotron and in the pro­ject­ed SIS-100. The elec­trons can po­ten­tial­ly ac­cu­mu­late in the space charge po­ten­tial of the long bunch­es. As an ex­treme case we study the ac­cu­mu­la­tion of elec­trons in a coast­ing beam under con­di­tions rel­e­vant in the SIS-18. Pre­vi­ous stud­ies of elec­tron clouds in coast­ing beams used Par­ti­cle-In-Cell (PIC) codes to de­scribe the gen­er­a­tion of the cloud and the in­ter­ac­tion with the ion beam. PIC beams ex­hib­it much larg­er fluc­tu­a­tion am­pli­tudes than real beams. The fluc­tu­a­tions heat the elec­trons. There­fore the ob­tained neu­tral­iza­tion de­gree is strong­ly re­duced, rel­a­tive to a real beam. In our sim­u­la­tion model we add a Langevin term to the elec­tron equa­tion of mo­tion in order to ac­count for the heat­ing pro­cess. The ef­fect of nat­u­ral beam fluc­tu­a­tions on the neu­tral­iza­tion de­gree is stud­ied. The mod­i­fi­ca­tion of the beam re­sponse func­tion as well as the sta­bil­i­ty lim­its in the pres­ence of the elec­trons is dis­cussed. Fi­nal­ly we will also ad­dress the elec­tron ac­cu­mu­la­tion in long bunch­es.

• W.M. Daqa
  IAP, Frankfurt am Main
• O. Boine-Frankenheim, I. Hofmann, V. Kornilov, J. Struckmeier
  GSI, Darmstadt

For high cur­rent syn­chrotrons and for the SIS18 op­er­a­tion as boost­er of the pro­ject­ed SIS100 it is im­por­tant to im­prove the mul­ti-turn in­jec­tion ef­fi­cien­cy. This can be achieved by cou­pling the trans­verse planes with skew quadrupoles, which can move the par­ti­cles away from the sep­tum. Lin­ear be­ta­tron cou­pling by skew quadrupole com­po­nents in SIS18 in­clud­ing space charge ef­fect was stud­ied in an ex­per­i­ment using dif­fer­ent di­ag­nos­tic meth­ods dur­ing the cross­ing of the dif­fer­ence cou­pling res­o­nance. The beam loss was mea­sured using a fast cur­rent trans­former, the trans­verse emit­tance ex­change was ob­served using a resid­u­al gas mon­i­tor and the cou­pled tunes were ob­tained from the Schot­tky noise spec­trum. We com­pared the ex­per­i­men­tal re­sults with sim­u­la­tion using PARM­TRA which is a code de­vel­oped at GSI.

• V. Kornilov, O. Boine-Frankenheim
  GSI, Darmstadt
• V.V. Kapin
  ITEP, Moscow

Oc­tupole mag­nets can be used as a pas­sive cure against trans­verse col­lec­tive in­sta­bil­i­ties. The oc­tupole field cre­ates a be­ta­tron fre­quen­cy spread due to am­pli­tude-de­pen­dent tune shift and thus en­hances Lan­dau damp­ing. The draw­back is the re­duc­tion of the dy­nam­ic aper­ture (DA). Ul­ti­mate­ly, a bal­ance be­tween col­lec­tive damp­ing and DA must be found. Here we anal­yse the trans­verse co­her­ent in­sta­bil­i­ty thresh­olds in SIS100 with oc­tupoles and non­lin­ear space-charge taken into ac­count. As the major impedance sources at low fre­quen­cies, the re­sis­tive wall and the kick­ers are con­sid­ered. A coast­ing beam is as­sumed, which re­sults in a con­ser­va­tive sta­bil­i­ty es­ti­ma­tion. On the other hand, we sim­u­late the DA of the SIS100 lat­tice using the MADX code, with sys­tem­at­ic mul­ti­pole er­rors, ran­dom mul­ti­pole er­rors, and closed-or­bit er­rors taken into ac­count.

• O. Boine-Frankenheim
  GSI, Darmstadt

The FAIR ac­cel­er­a­tor pro­ject at GSI should in­crease the in­ten­si­ty of pri­ma­ry pro­ton and heavy ion beams by up to two or­ders of mag­ni­tude, rel­a­tive to the ex­ist­ing GSI fa­cil­i­ty. In ad­di­tion to the de­sign of the new syn­chrotron SIS-100 and the stor­age rings, the in­ten­si­ty up­grade of the SIS-18 syn­chrotron plays a key role for the FAIR pro­ject. Re­cent­ly a new record beam in­ten­si­ty for in­ter­me­di­ate charge state ura­ni­um ions has been achieved in the SIS-18. Still sev­er­al chal­lenges re­lat­ed to beam in­ten­si­ty ef­fects and phase space con­ser­va­tion have to be mas­tered in order to reach the beam pa­ram­e­ters re­quired for the in­jec­tion into SIS-100. In SIS-100 beam loss con­trol and ma­chine pro­tec­tion are of major con­cern. Lost en­er­get­ic heavy ions can cause a more se­vere dam­age of ac­cel­er­a­tor com­po­nents than the cor­re­spond­ing amount of pro­tons. Grad­u­al beam loss of en­er­get­ic ions is ex­pect­ed to occur in SIS-100 main­ly dur­ing slow ex­trac­tion of in­tense beams. Co­her­ent trans­verse in­sta­bil­i­ties in­duced by the beam pipe impedance are a po­ten­tial cause of fast beam loss and emit­tance in­crease. Cures and pro­tec­tion mea­sures to­geth­er with the re­sult of sim­u­la­tion stud­ies will be sum­ma­rized.

Slides

• S. Sorge, O. Boine-Frankenheim, G. Franchetti
  GSI, Darmstadt
• A. Bolshakov
  ITEP, Moscow

The heavy ion syn­chrotron SIS-100 will play a key role with­in the fu­ture FAIR pro­ject un­der­way at GSI. Al­though this syn­chrotron is op­ti­mized for fast ex­trac­tion, also slow ex­trac­tion will be used. Slow ex­trac­tion is based on beam ex­ci­ta­tion due to a third order res­o­nance. The spread in the par­ti­cle mo­men­ta gen­er­at­ing a tune spread caus­es par­ti­cle loss lead­ing to an ir­ra­di­a­tion of the ma­chine es­pe­cial­ly in a high-cur­rent op­er­a­tion. A major part of the loss­es is as­sumed to occur at the elec­tro-stat­ic sep­a­ra­tor. In the pre­sent study we apply a track­ing method to model the ex­trac­tion pro­cess to pre­dict the loss­es, where, in a first step, high cur­rent ef­fects are not taken into ac­count.