Studies of the regenerative BBU at the JLab FEL Upgrade (Part I) - PowerPoint PPT Presentation

Studies of the regenerative BBU at the JLab FEL Upgrade (Part I) Eduard Pozdeyev, Chris Tennant Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

Outline 1. Theoretical model of the BBU: fresh look at the problem 2. Measurements techniques and results 3. Comparison of the experimental data to the model 4. Summary and Plans Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

Energy transfer from the beam to HOM 1 st pass ∫ = = ϕ = = ϕ max V ( r a ) V cos( ) E ( r a ) dz cos( ) a z cV − sin( ϕ a ) ω V a ′ = = ⊥ x V V b b B 2 nd pass x = m 12 x ' E x x q x ∆ = − ϕ + ω + U qV cos( T ) V a r q a 2 a ⎛ ⎞ ω ω 2 ⎛ ⎞ R x = ⎜ ⎟ ⎜ ⎟ 2 V q qa ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ 2 c Q a Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

BBU threshold equation & = & − = ∆ + ∆ ⋅ − U U P U U f P cav beam c in out b c 2 V = a P ⎛ ⎞ c R ( ω ⎜ ⎟ 2 2 / c ) a Q ⎜ ⎟ L ⎝ ⎠ Q ⎛ ⎞ ⎜ ⎟ ω ⎜ ⎟ 2 dU V m c sin( T ) 1 = − + a 12 r I ⎜ ⎟ ω ⎛ ⎞ b 2 dt a V 2 R ⎜ ⎟ ω ⎜ ⎟ 2 b ( / c ) Q ⎜ ⎟ ⎜ ⎟ L ⎝ ⎠ ⎝ ⎠ Q The condition dU/dt=0 yields the threshold m 12 sin( ω T r )<0 – unstable 2 V = − b I m 12 sin( ω T r )>0 – “pseudo”-stable ⎛ ⎞ th R ω ⎜ ⎟ ω ( / c ) ⎜ ⎟ Q m sin( T ) L 12 r (J. Bisognano, G. Krafft, S. Laubach, ⎝ ⎠ Q 1987, N. Sereno, 1989) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

Two-dimensional case r r → ⋅ = α + α x d n x cos( ) y sin( ) d =(x,y) is the 2D displacement vector, α is the HOM angle, M(2x2) -> M(4x4) 2 V = − b I ⎛ ⎞ th R ω ⎜ ⎟ ω * ( / c ) Q m sin( T ) ⎜ ⎟ L 12 r ⎝ ⎠ Q = α + + α α + α * 2 2 m m cos ( ) ( m m ) sin( ) cos( ) m sin ( ) 12 12 14 32 34 (E. Pozdeyev, 2004) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

Voltage evolution above and below I th ω 2 ⎛ ⎞ ⎛ ⎞ 2 V a R ⎜ ⎟ = ω ⎜ ⎟ U ⎜ ⎟ ⎝ ⎠ 2 ⎝ ⎠ a c Q ω − dU I I = − th dt U Q I L th ⎛ ⎞ ω − I I ⎜ ⎟ = − th b U U exp t ⎜ ⎟ 0 ⎝ ⎠ Q I L th ⎛ ⎞ ω − I I ⎜ ⎟ = − th b V V exp t ⎜ ⎟ 0 ⎝ ⎠ 2 Q I L th I I = τ = τ th th Q Q � − − eff L eff 0 I I I I th th Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

JLab FEL Upgrade Energy(MeV) 80-200 Cavities of Zone 3 have higher Charge per bunch (pC) 135 accel. gradient than Zone 2,4. The Q of dipole HOMs is also Bunch rep.rate (MHz) 4-75 higher. HOMs of Zone 3 impose Average current (mA) 10 BBU limit. Laser power (kW) 10 IR wiggler Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

Questions •How well do the model and simulations describe the BBU and the beam behavior •Can we reliably predict the BBU threshold below the threshold •Can we suppress the BBU (C. Tennant, this seminar Part II) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

Direct measurements of the BBU threshold Schottky diodes where attached to all the HOM ports. The voltage from the diodes was monitored on oscilloscopes. (K. Jordan) HOM port Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

Direct measurements of the BBU threshold 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -5.00E-08 -2.50E-08 0.00E+00 2.50E-08 5.00E-08 Schottky diode signal (blue) yields a cavity where BBU happens, FFT of the voltage (red) signal yields the HOM frequency: Cav 7, F hom =2106 MHz, Ith=2.7 mA Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

Beam Transfer Function (BTF) measurements Measuring Q(I) for several beam NWA current values and using the formula (S21) I = th Q Q − eff L I I th one can predict the BBU threshold below the threshold. +’s: 1) stronger signal 2) no need for RF amplifier 3) no need for kicker -’s: cross-talk can complicate Q-measurements Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

Beam Transfer Function (BTF) measurements Cav 7, F hom =2106 MHz -1 10 2.5 mA 0.2 2.0 mA 1.5 mA 1.0 mA 0.5 mA 0.15 y = -0.0583x + 0.167 -2 10 1/Q 0.1 S 21 0.05 -3 10 0 0 0.5 1 1.5 2 2.5 3 I (mA) -4 10 -1000 -500 0 500 1000 dF(Hz) Projected threshold current is 2.86 mA Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

HOM voltage growth rate measurements Measuring HOM voltage growth rate for several beam current values and using the formula: HOM port I τ = τ th − eff 0 I I th one can calculate the BBU threshold above the threshold. Note, knowing τ 0 is not necessary Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

HOM voltage growth rate measurements 0 10 3.6 mA invert 4.2 mA 0 5.0 mA + adjust + -0.05 V (Volt) P(mW) log -1 10 -0.1 3.6 mA 4.2 mA 5.0 mA -2 -0.15 10 -0.015 -0.01 -0.005 0 0.005 0.01 -0.01 -0.005 0 0.005 t (sec) t(sec) 2000 1600 y = 631.24x - 1645.2 1/t (1/sec) 1200 I th =2.61 mA Cav 7, F hom =2106 MHz 800 400 0 0 1 2 3 4 5 6 I (mA) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

What about other HOMs? I=5mA 0.002 0.001 0 Cav. 3, F=1786.206 -0.001 V -0.002 BTF measurements: the HOM -0.003 is very far from the threshold -0.004 -0.005 (BTF-predicted I th =34 mA) -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 t (sec) 0.002 0.001 Cav. 8, F=1881.481 0 -0.001 BTF measurements inconclusive. V -0.002 Cross-talk prevented us from -0.003 -0.004 taking accurate BTF data. -0.005 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 t (sec) We are not sure what causes this voltage rise Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

The “pseudo”-stable region (m 12 sin( ω T r )>0 ) 2 V = − b I ⎛ ⎞ th R ω ⎜ ⎟ ω ( / c ) Q m sin( T ) ⎜ ⎟ L 12 r ⎝ ⎠ Q For m 12 sin( ω T r )>0, this formula yields a negative threshold. Although it sounds bizarre, the negative threshold current can be “measured” and, thus, has a physical meaning… Sort of… According to the Q-formula, − I I I = = = th th th Q Q Q Q − − − + eff L L L I I I I I I th th th the effective Q has to become smaller as the beam current increases Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

The “pseudo”-stable region (m 12 sin( ω T r )>0 ) Cav 7, mode F=2116.584 MHz -50 0.0 mA 0.5 mA 0.25 -55 1.0 mA 1.5 mA -60 0.2 -65 0.15 1/Q y = 0.0467x + 0.1512 -70 0.1 S 21 -75 0.05 -80 0 -85 0 0.5 1 1.5 2 I (mA) -90 -95 -2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500 Ith=-3.24 mA dF(Hz) The mode that was causing the BBU in Spring 2004, F=2114.156 in Cav. 4 was also “stable” (I th =-9.5 mA) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy

Comparison to the analytical formula Dave Douglas’ original Excel spreadsheet: November 2004 Measured Calculated Cav.7 f=2106 (if y-polarized): 2.7 mA 3.3 mA Cav.7 f=2116 (if x-polarized): -3.24 mA -14 mA Cav.4 f=2114 (if x-polarized): -9.5 mA -5.4 mA Cav.3 f=1786 (if x-polarized): 34 mA 100 mA Cav.8 f=1881 (if x-polarized): ? 63 mA Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy