IMPEDANCE MEASUREMENT OF ATF DR H.Hayano, E.S.Kim, K.Kubo, T.Naito, K.Oide, N.Terunuma and J.Urakawa, KEK, Ibaraki, Japan S. Kashiwagi,The Graduate Univ. for Advanced Studies, Ibaraki, Japan T. Okugi, Tokyo Metro. Univ., Tokyo, Japan Abstract The purpose of the damping ring in the KEK acceler- ator test facility (ATF) is to develop the technologies to achieve a lower emittance beam that required in the future linear collider such as JLC. To avoid the unacceptable emittance growth, vac- uum chambers were designed to have a low impedance to suppress single bunch instabilities. The actual impedance of the ring was evaluated by measuring the intensity dependence of the bunch length. We report the results of the present impedance measurement of the ATF damping ring. 1 IMPEDANCE 1.1 Vacuum Chamber and Impedance Vacuum chambers for the ATF damping ring, circum- ference is 138.6 m, were designed to achieve a low impedance ring [1]. For two arc sections of the ring, we keep the chamber cross section as a circle of 24 mm diameter [2]. All gaps were shielded with a finger con- tact and a metal-ring gasket. For the straight sections, there are many objects that changes the chamber cross section such as cavities, photon masks, wiggler and septum chambers. The contribution to the impedances of these vacuum components were estimated [1, 3, 4] by using numerical code ABCI, MAFIA and MASK30. Table 1 shows the summary of this estimation. Table 1: Impedance sources in the ATF damping ring; the bunch length was assumed to be 6.8 mm. Components Number L(nH) BPM 96 4.80 Bellows 64 2.03 Photon Masks 16 3.61 Tapers 5 1.42 Septum 1 0.62 RF cavity 2 0.69 RF absorber 4 0.67 Total 13.9 By adding up the all wake potentials calculated in this estimation and multiplying them with the number of each component, we got the total longitudinal wake potential as shown in Fig. 1. It shows the total contri- bution is clearly inductive. Therefore we proceed the analysis with an inductive impedance model. -8 -6 -4 -2 0 2 4 6 8 0 0.02 0.04 0.06 0.08 0.1 Wake Potential (V/pC) Distance from a bunch head (m) Charge Distribution Longitudinal Wake potential Figure 1: Total longitudinal wake potential in ATF damping ring. 1.2 Inductive impedance The self-consistent beam current distribution in an electron machine, below the turbulent threshold, is given by [5] I (t)= K(- t 2 2σ 2 o + 1 ˙ V RF σ 2 o  t o V ind (t ′ )dt ′ ), (1) with σ o the natural bunch length, ˙ V RF the slope of the RF voltage at the position of the bunch and V ind the transient induced voltage. Taking the derivative of both sides of Eq.(1) yields an alternative form of it: ˙ I I = - t σ 2 o + V ind ˙ V RF σ 2 o . (2) For purely inductive object the induced voltage is given by V ind = -LdI/dt, with the constant L the inductance. Eq.(2) can be written as dy dx = - xy 1+ y , (3) with the variables of x = t/σ o , y = LI/( ˙ V RF σ o 2 ). The complete integral of y, the normalized charge Γ, becomes Γ=  ∞ −∞ dx y = LQ ˙ V RF σ o 3 , where Q is a total charge in the bunch. The numerical solutions of Eq.(3), for several values of Γ, give the 481