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Stability analysis with MIA / 1

Stability analysis with MIA / 1. The so-called Machine Independent Analysis has been refined by improving the data treatment. The BPM data is put in the form of a matrix B. The reading of BPM i feor measurement j represented by b i j . Each trajectory corresponds to a line of B :.

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Stability analysis with MIA / 1

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  1. Stability analysis with MIA / 1 The so-called Machine Independent Analysis has been refined by improving the data treatment. The BPM data is put in the form of a matrix B. The reading of BPM i feor measurement j represented by bij . Each trajectory corresponds to a line of B : N = no. of BPMs M = no. measurements assume M > N ! time space The improvement consists in subtracting the average position at each BPM from every point and by re-normalizing the matrix by 1/sqrt(N*M). The later step avoids the problem that the eigenvalues increase with the number of trajectories. In addition about 5 ‘crazy’ BPMs (giving large [> 30 mm] readings) are discarded. TI8 analysis / J. Wenninger

  2. Stability analysis with MIA / 2 The matrix B is then again decomposed by SVD into : • where : • U is a matrix of normalized and orthogonal time patterns. • V is a matrix of normalized and orthogonal space patterns. • W is a diagonal matrix with the eigenvalues of the space patterns. As a consequence of the improved data filtering, large eigenvalues associated with the static trajectory and bad BPM readings are now removed. As a consequence the signal should appear more clearly above the noise. TI8 analysis / J. Wenninger

  3. Eigenvalue spectrum The eigenvalue spectrum in the horizontal plane indicates a clear signal above the noise floor for the first eigenvalue. This eigenvalue corresponds to a trajectory that is compatible with a kick at the septum (as presented at a previous meeting). TI8 analysis / J. Wenninger

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