Studies of the Regenerative BBU Studies of the Regenerative BBU Instability at the JLab FEL Upgrade Instability at the JLab FEL Upgrade Chris Tennant and Eduard Pozdeyev Center for Advanced Studies of Accelerators Jefferson Laboratory CASA Seminar March 4, 2005 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
Outline � Methods of BBU Suppression � Beam Optical Schemes • Theory • Experimental � Phase trombone � Pseudo-Reflector � Q -Damping Schemes • Active damping circuit • 3-Stub tuner � Summary and Future Plans Thomas Jefferson National Accelerator Facility Page 2 Operated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
Analytic Model for Multipass BBU • For the case of a two-pass ERL with a single cavity, containing a single HOM the equation for the BBU threshold current is given by 2 V = − beam I ω threshold * M k ( R Q ) Q sin( T ) recirc ≡ α + + α α + α * 2 2 M M cos ( M M ) sin cos M sin 12 14 32 34 � Alter beam optics � Inject at higher energy � Change phase advance � Change HOM frequency � Reflect betatron planes � Change recirculation time � Rotate betatron planes � Damp HOM quality factor where V beam is the beam voltage at the cavity, k is the wavenumber ( ω /c ) of the HOM, (R/Q)Q is the shunt impedance, T recirc is the recirculation time and the M ij are the elements of the recirculation transport matrix Thomas Jefferson National Accelerator Facility Page 3 Operated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
Effect of Reflecting Optics 1 ∝ − I threshold Recall… α + + α α + α 2 2 M cos ( M M ) sin cos M sin 12 14 32 34 I. Reflecting Optics will Suppress BBU if… I. The transfer matrix from an unstable cavity back to itself takes the form = = ⎛ ⎞ M M 0 0 M ⎜ ⎟ 12 34 ⎜ ⎟ = ⎝ ⎠ M 0 M M 14 32 α α = II. The HOMs are oriented at either 0 or 90 degrees sin cos 0 1500 Theory Simulation 1000 If α is different from 0 or 90 Threshold Current degrees, the effectiveness of Threshold Current (mA) 500 reflecting optics in BBU Stable Stable 0 suppression rapidly diminishes. -500 -1000 -1500 0 50 100 150 200 250 300 350 HOM Orientation w.r.t. the x-Axis HOM Orientation with Respect to the x-Axis (degrees) Thomas Jefferson National Accelerator Facility Page 4 Operated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
Effect of Rotating Optics 1 ∝ − I threshold Recall… α + + α α + α 2 2 M cos ( M M ) sin cos M sin 12 14 32 34 II. Rotating Optics will Suppress BBU if… I. The transfer matrix from an unstable cavity back to itself takes the form = = ⎛ ⎞ M M 0 0 M ⎜ ⎟ 12 34 ⎜ ⎟ − = − ⎝ ⎠ M 0 M M 14 32 A rotation is effective regardless of the orientations of the HOMs y ’ y � First pass ' The offending mode imparts an r angular deflection, α , to a bunch x ’ x Second pass (after rotation) α α The resultant displacement will be � orthogonal to the offending HOM. The bunch will be unable to couple r energy to the mode that caused the deflection. ( x ’ , y ’ ) (- y , x ) Thomas Jefferson National Accelerator Facility Page 5 Operated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
Beam Optical Control of BBU On-axis magnetic field kicks First Pass Second Pass: Nominal Optics electron beam in y direction on the first pass via the The y kick results in a y displacement y on the second pass through the cavity. This puts the electrons in a region of dipole HOM z � � � longitudinal field and they can deposit � energy into the HOM field Linac axis HOM axial electric field (90 ° out of phase with B field) x Transverse magnetic y field of dipole HOM � � Linac axis � z � Second Pass: 90 ° Rotated Optics � � The y kick results in an x displacement on � � the second pass through the cavity. The bunches are in a region of zero longitudinal field and they cannot give energy to the x HOM field. The feedback between the beam and HOM has been broken! Courtesy T. Smith (HEPL) Thomas Jefferson National Accelerator Facility Page 6 Operated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
Skew-Quadrupole Reflector in the FEL • 5 skew-quadrupoles were installed in the backleg of the FEL to ( locally ) interchange the x and y phase spaces (D. Douglas) -3 1.4x10 1.2 1.0 Beam Envelopes (m ) 0.8 0.6 0.4 0.2 0.0 wiggler Skew-quad reflector Thomas Jefferson National Accelerator Facility Page 7 Operated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
Local Reflector 2106 MHz in Cavity 7 • With the reflector activated, we also investigated the Inverse Q eff stability of several other potentially dangerous HOMs Q L = 5.9e+06 I th = 9.2 mA 0 1 2 3 4 5 Average Beam Current (mA) BTF of 2106 MHz with Reflector ON 2116 MHz in Cavity 7 2114 MHz in Cavity 4 I = 0.0 mA I = 3.5 mA I = 4.0 mA Q L = 6.4e+06 Q L = 5.4e+06 I = 4.5 mA I th = -14 mA I = 5.0 mA I th = -8 mA Inverse Q eff Magnitude Inverse Q eff 0 1 2 3 4 5 0 1 2 3 4 5 Average Beam Current (mA) Average Beam Current (mA) Frequency Thomas Jefferson National Accelerator Facility Page 8 Operated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
Local Reflector with a Change in Phase Advance • Ideally we would like to create a pure 90 degree rotation from the unstable cavity back to itself 2106 MHz with Reflector ON and � Can you create a “ global ” rotation Phase Advance Changed with a “ local ” reflector? � Yes . By decreasing the vertical phase advance and then activating Inverse Q eff the local reflector, you can create a 90 degree rotation from the middle of Zone 3 back to itself (D. Douglas) . • For our measurements, the vertical Q L = 5.0e+06 phase advance was changed. Only I th = -17 mA after the difference orbit measure- 0.5 1.0 1.5 2.0 2.5 ments have been analyzed, will we Average Beam Current (mA) know what kind of transfer matrix was generated with this change in phase Because of the limited time setting up this advance… configuration, the transmission was not good. Thomas Jefferson National Accelerator Facility Page 9 Operated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
What BBU “Looks Like” PLAY Thomas Jefferson National Accelerator Facility Page 10 Operated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
Phase Trombone 1 I threshold ∝ Recall… M 12 ,( 34 ) • By all indications the 2106 MHz HOM is a vertically polarized mode • We change 4 vertically focusing quadrupoles in the recirculator to vary the vertical phase advance Quads changed +200 G Quads changed +300 G I beam = 6.0 mA I beam = 0.5 mA I beam = 1.5 mA I beam = 2.5 mA I beam = 3.5 mA I beam = 4.5 mA I beam = 4.0 mA I beam = 3.5 mA I beam = 5.0 mA I beam = 0.0 mA Stable Unstable I th = -7 mA I th = 12 mA Magnitude Magnitude Frequency Frequency Thomas Jefferson National Accelerator Facility Page 11 Operated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
Phase Trombone (cont’d…) • We were able to easily change the quadrupole strengths from their nominal settings from -200 G to +300 G • We observe a (1/ sin ) trend in the threshold current from measurements ⎡ ⎤ 1 1 1 ∝ ∝ ⎢ ⎥ I I threshold ω threshold β β ∆ ψ ω ⎣ sin( T ) ⎦ M sin( T ) sin( ) HOM r 34 HOM r 1 2 15 15 10 10 Threshold Current (mA) Threshold Current (mA) 5 5 0 0 -5 -5 -10 -10 -15 -15 2105.0 2105.5 2106.0 2106.5 -400 -200 0 200 400 HOM Frequency (MHz) Change in Quadrupole Strength (G) Thomas Jefferson National Accelerator Facility Page 12 Operated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
Q -Damping Circuit Directional Circulator Pre-amplifier Coupler Concept: couple power from one of the HOM ports, shift it 180 degrees in phase, amplify the signal and feed it BPF back through the same HOM port. 20 dB Variable Variable Bandpass Circulator Attenuator Phase Shifter Filter “Tuning Knobs”: the circuit is Network Analyzer optimized by carefully tuning the phase HOM 1 and gain of the feedback loop 20 dB Port 2 Port 1 HOM 2 10 dB 10 dB Directional Coupler Active damping of an HOM located at 2106 MHz. The effect of the damping (right picture) is to decrease the loaded Q by a factor of ~ 10 . Q L = 0.5 x 10 6 Q L = 5.8 x 10 6 Thomas Jefferson National Accelerator Facility Page 13 Operated by the Southeastern Universities Research Association for the U.S. Department of Energy C. Tennant CASA Seminar
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