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10.440000 0.0 Td (\177\)f\177w ) Tj 27.480000 0.0 Td (sin\(\177b\) ) Tj ET BT 1.000000 0 0 1 109.320000 617.760000 Tm 3 Tr 0 0 0 rg /F0 15.480000 Tf 0.000000 0.0 Td (-\(vz ) Tj 24.000000 0.0 Td (+ ) Tj 10.680000 0.0 Td (\177\)fiw ) Tj 27.480000 0.0 Td (sin\(\177b- ) Tj 36.120000 0.0 Td (\(2kx- ) Tj ET BT 1.000000 0 0 1 278.760000 623.040000 Tm 3 Tr 0 0 0 rg /F0 10.200000 Tf 0.000000 0.0 Td (\(6\) ) Tj ET BT 1.000000 0 0 1 106.080000 586.200000 Tm 3 Tr 0 0 0 rg /F0 15.120000 Tf 0.000000 0.0 Td (= ) Tj 33.720000 0.0 Td (,.,t ) Tj 13.200000 0.0 Td (+ ) Tj 10.080000 0.0 Td (at- ) Tj 39.480000 0.0 Td (- ) Tj 37.560000 0.0 Td (cos\(\) ) Tj ET BT 1.000000 0 0 1 143.640000 568.680000 Tm 3 Tr 0 0 0 rg /F0 13.920000 Tf 54.720000 0.0 Td (- ) Tj 32.160000 0.0 Td (- ) Tj 9.240000 0.0 Td (o\)\) ) Tj ET BT 1.000000 0 0 1 109.200000 564.120000 Tm 3 Tr 0 0 0 rg /F0 14.640000 Tf 23.760000 0.0 Td (+ ) Tj ET BT 1.000000 0 0 1 279.000000 569.400000 Tm 3 Tr 0 0 0 rg /F0 10.200000 Tf 0.000000 0.0 Td (\(7\) ) Tj ET BT 1.000000 0 0 1 50.160000 547.440000 Tm 3 Tr 0 0 0 rg /F0 11.040000 Tf 0.000000 0.0 Td (where ) Tj 30.240000 0.0 Td (f\177w ) Tj 18.120000 0.0 Td (= ) Tj 12.960000 0.0 Td (ebb. ) Tj 26.520000 0.0 Td (For ) Tj ET BT 1.000000 0 0 1 115.800000 545.400000 Tm 3 Tr 0 0 0 rg /F0 3.840000 Tf 0.000000 0.0 Td (m ) Tj ET BT 1.000000 0 0 1 50.520000 534.840000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (One ) Tj 21.000000 0.0 Td (obtains ) Tj 35.400000 0.0 Td (from ) Tj 24.840000 0.0 Td (\(5\) ) Tj ET BT 1.000000 0 0 1 63.840000 506.400000 Tm 3 Tr 0 0 0 rg /F0 8.040000 Tf 0.000000 0.0 Td (dt ) Tj 9.000000 0.0 Td (2 ) Tj ET BT 1.000000 0 0 1 82.800000 511.080000 Tm 3 Tr 0 0 0 rg /F0 11.400000 Tf 0.000000 0.0 Td (+ ) Tj 9.840000 0.0 Td (kv\361aw[sin\(\177b\) ) Tj 63.600000 0.0 Td (+ ) Tj 9.840000 0.0 Td (sin\(\177b ) Tj 25.800000 0.0 Td (- ) Tj 10.080000 0.0 Td (\(2kx ) Tj 22.320000 0.0 Td (- ) Tj 9.240000 0.0 Td (0\)\)] ) Tj 19.680000 0.0 Td (- ) Tj 10.080000 0.0 Td (0 ) Tj 15.960000 0.0 Td (\(8\) ) Tj ET BT 1.000000 0 0 1 50.520000 490.560000 Tm 3 Tr 0 0 0 rg /F0 10.800000 Tf 0.000000 0.0 Td (Equation ) Tj 44.040000 0.0 Td (\(8\) ) Tj 15.240000 0.0 Td (has ) Tj 17.880000 0.0 Td (the ) Tj 17.040000 0.0 Td (basic ) Tj 25.080000 0.0 Td (form ) Tj 23.520000 0.0 Td (of ) Tj 11.280000 0.0 Td (the ) Tj 16.800000 0.0 Td (pendulum ) Tj 46.560000 0.0 Td (equa- ) Tj ET BT 1.000000 0 0 1 50.400000 478.920000 Tm 3 Tr 0 0 0 rg /F0 10.560000 Tf 0.000000 0.0 Td (tion ) Tj 20.400000 0.0 Td (where ) Tj 28.680000 0.0 Td (the ) Tj 17.160000 0.0 Td (phase ) Tj 27.720000 0.0 Td (angles ) Tj 29.880000 0.0 Td (oscillate ) Tj 38.160000 0.0 Td (around ) Tj 33.360000 0.0 Td (an ) Tj 13.320000 0.0 Td (equilib- ) Tj ET BT 1.000000 0 0 1 50.400000 466.800000 Tm 3 Tr 0 0 0 rg /F0 11.400000 Tf 0.000000 0.0 Td (rium ) Tj 23.760000 0.0 Td (position, ) Tj 41.280000 0.0 Td (with ) Tj 22.560000 0.0 Td (frequency ) Tj 45.480000 0.0 Td (w ) Tj 8.640000 0.0 Td (2 ) Tj 7.560000 0.0 Td (= ) Tj 10.440000 0.0 Td (k\177wv\361. ) Tj 38.280000 0.0 Td (\(8\) ) Tj 15.000000 0.0 Td (can ) Tj 17.760000 0.0 Td (be ) Tj ET BT 1.000000 0 0 1 50.400000 454.680000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (expressed ) Tj 45.360000 0.0 Td (in ) Tj 12.000000 0.0 Td (a ) Tj 8.280000 0.0 Td (more ) Tj 25.440000 0.0 Td (simplified ) Tj 45.360000 0.0 Td (way ) Tj 20.520000 0.0 Td (as ) Tj ET BT 1.000000 0 0 1 89.040000 427.080000 Tm 3 Tr 0 0 0 rg /F0 7.920000 Tf 0.000000 0.0 Td (dt ) Tj 9.000000 0.0 Td (2 ) Tj ET BT 1.000000 0 0 1 86.880000 431.760000 Tm 3 Tr 0 0 0 rg /F0 11.160000 Tf 0.000000 0.0 Td (--+ ) Tj 30.960000 0.0 Td (kvxaw[sin\(\177\) ) Tj 63.480000 0.0 Td (+ ) Tj 9.720000 0.0 Td (sin\(\177b- ) Tj 35.040000 0.0 Td (7\)] ) Tj 15.720000 0.0 Td (- ) Tj 10.080000 0.0 Td (0 ) Tj 27.720000 0.0 Td (\(9\) ) Tj ET BT 1.000000 0 0 1 50.760000 409.440000 Tm 3 Tr 0 0 0 rg /F0 12.600000 Tf 0.000000 0.0 Td (where ) Tj 29.040000 0.0 Td (if\(t\) ) Tj 20.520000 0.0 Td (= ) Tj 10.680000 0.0 Td (2[\(a ) Tj 21.720000 0.0 Td (-w\)t- ) Tj 37.080000 0.0 Td (q]. ) Tj 17.040000 0.0 Td (\(9\) ) Tj 15.360000 0.0 Td (can ) Tj 18.360000 0.0 Td (be ) Tj 13.560000 0.0 Td (expressed ) Tj 44.640000 0.0 Td (as ) Tj ET BT 1.000000 0 0 1 99.600000 381.840000 Tm 3 Tr 0 0 0 rg /F0 21.480000 Tf 0.240000 0.0 Td (d20 ) Tj 21.720000 0.0 Td (- ) Tj 9.720000 0.0 Td (2kv\361awsin\(O\)sin\(\177\) ) Tj 98.400000 0.0 Td (= ) Tj 10.320000 0.0 Td (0 ) Tj 34.800000 0.0 Td (\(10\) ) Tj ET BT 1.000000 0 0 1 101.880000 381.000000 Tm 3 Tr 0 0 0 rg /F0 8.040000 Tf 0.000000 0.0 Td (dt ) Tj 9.000000 0.0 Td (2 ) Tj ET BT 1.000000 0 0 1 50.880000 363.960000 Tm 3 Tr 0 0 0 rg /F0 12.000000 Tf 0.000000 0.0 Td (where ) Tj 30.360000 0.0 Td (O ) Tj 12.120000 0.0 Td (= ) Tj 13.440000 0.0 Td (2 ) Tj -0.720000 0.0 Td (\177 ) Tj 9.360000 0.0 Td (+ ) Tj 11.160000 0.0 Td (\177 ) Tj 9.840000 0.0 Td (- ) Tj 10.080000 0.0 Td (\177b. ) Tj 16.800000 0.0 Td (This ) Tj 23.640000 0.0 Td (is ) Tj 10.920000 0.0 Td (of ) Tj 12.120000 0.0 Td (the ) Tj 18.000000 0.0 Td (form ) Tj 24.360000 0.0 Td (of ) Tj 12.240000 0.0 Td (a ) Tj 9.120000 0.0 Td (sim- ) Tj ET BT 1.000000 0 0 1 50.760000 353.160000 Tm 3 Tr 0 0 0 rg /F0 10.680000 Tf 0.000000 0.0 Td (ple ) Tj 15.960000 0.0 Td (pendulum ) Tj 47.160000 0.0 Td (with ) Tj 22.680000 0.0 Td (a ) Tj 7.800000 0.0 Td (time ) Tj 22.560000 0.0 Td (modulated ) Tj 49.440000 0.0 Td (length ) Tj 30.120000 0.0 Td (or ) Tj 11.640000 0.0 Td (gravita- ) Tj ET BT 1.000000 0 0 1 51.000000 342.000000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (tional ) Tj 28.680000 0.0 Td (accelaration. ) Tj 60.480000 0.0 Td (The ) Tj 20.760000 0.0 Td (above ) Tj 28.440000 0.0 Td (pendulum ) Tj 46.920000 0.0 Td (equation ) Tj 40.800000 0.0 Td (can ) Tj ET BT 1.000000 0 0 1 50.880000 330.960000 Tm 3 Tr 0 0 0 rg /F0 8.160000 Tf 0.000000 0.0 Td (be ) Tj 13.800000 0.0 Td (derived ) Tj 35.400000 0.0 Td (from ) Tj 24.120000 0.0 Td (Hamiltonian ) Tj ET BT 1.000000 0 0 1 113.040000 317.040000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (1 ) Tj 10.800000 0.0 Td (dO ) Tj ET BT 1.000000 0 0 1 88.440000 304.560000 Tm 3 Tr 0 0 0 rg /F0 16.200000 Tf 0.000000 0.0 Td (H ) Tj 12.480000 0.0 Td (- ) Tj 11.280000 0.0 Td (\177\(_\177\)2 ) Tj 37.080000 0.0 Td (+ ) Tj 9.840000 0.0 Td (2kv\361aw ) Tj 37.560000 0.0 Td (cos\(O\)sin\(\177\) ) Tj 78.360000 0.0 Td (\(11\) ) Tj ET BT 1.000000 0 0 1 51.120000 289.680000 Tm 3 Tr 0 0 0 rg /F0 10.440000 Tf 0.000000 0.0 Td (which ) Tj 28.080000 0.0 Td (simply ) Tj 31.440000 0.0 Td (has ) Tj 17.280000 0.0 Td (the ) Tj 16.440000 0.0 Td (form ) Tj 23.160000 0.0 Td (of ) Tj 10.680000 0.0 Td (the ) Tj 16.440000 0.0 Td (standard ) Tj 40.800000 0.0 Td (Hamiltonian. ) Tj ET BT 1.000000 0 0 1 51.120000 279.000000 Tm 3 Tr 0 0 0 rg /F0 9.480000 Tf 0.000000 0.0 Td (We ) Tj 17.280000 0.0 Td (can ) Tj 18.240000 0.0 Td (assume ) Tj 34.440000 0.0 Td (that ) Tj 21.960000 0.0 Td (around ) Tj 33.720000 0.0 Td (the ) Tj 17.040000 0.0 Td (resonance ) Tj 45.000000 0.0 Td (fixed ) Tj 24.000000 0.0 Td (points, ) Tj ET BT 1.000000 0 0 1 51.240000 266.040000 Tm 3 Tr 0 0 0 rg /F0 10.800000 Tf 0.000000 0.0 Td (and ) Tj 19.440000 0.0 Td (for ) Tj 15.720000 0.0 Td (sufficiently ) Tj 50.640000 0.0 Td (small ) Tj 26.400000 0.0 Td (wave ) Tj 24.600000 0.0 Td (amplitudes ) Tj 50.760000 0.0 Td (from ) Tj 24.480000 0.0 Td (\(5\) ) Tj ET BT 1.000000 0 0 1 149.400000 249.480000 Tm 3 Tr 0 0 0 rg /F0 10.440000 Tf 0.000000 0.0 Td (x ) Tj 8.880000 0.0 Td (= ) Tj 10.320000 0.0 Td (\177 ) Tj 7.440000 0.0 Td (+ ) Tj 9.480000 0.0 Td (fit ) Tj 89.760000 0.0 Td (\(12\) ) Tj ET BT 1.000000 0 0 1 63.120000 161.640000 Tm 3 Tr 0 0 0 rg /F0 7.680000 Tf 0.000000 0.0 Td (-k ) Tj 22.080000 0.0 Td (k ) Tj ET BT 1.000000 0 0 1 160.920000 174.480000 Tm 3 Tr 0 0 0 rg /F0 5.760000 Tf 0.000000 0.0 Td (y ) Tj ET BT 1.000000 0 0 1 253.080000 203.520000 Tm 3 Tr 0 0 0 rg /F0 3.960000 Tf 0.000000 0.0 Td (v ) Tj ET BT 1.000000 0 0 1 233.520000 171.240000 Tm 3 Tr 0 0 0 rg /F0 7.800000 Tf 0.000000 0.0 Td (k ) Tj 13.560000 0.0 Td (w ) Tj 12.120000 0.0 Td (\177 ) Tj ET BT 1.000000 0 0 1 50.520000 121.440000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (Figure ) Tj 39.600000 0.0 Td (1. ) Tj 19.800000 0.0 Td (Coordinate ) Tj 54.360000 0.0 Td (system ) Tj 35.280000 0.0 Td (for ) Tj 17.400000 0.0 Td (a ) Tj 10.560000 0.0 Td (single ) Tj 29.640000 0.0 Td (electron ) Tj ET BT 1.000000 0 0 1 50.520000 111.000000 Tm 3 Tr 0 0 0 rg /F0 9.840000 Tf 0.000000 0.0 Td (and ) Tj 19.920000 0.0 Td (two ) Tj 19.560000 0.0 Td (oppositely ) Tj 48.840000 0.0 Td (directed ) Tj 39.120000 0.0 Td (whistler ) Tj 38.280000 0.0 Td (mode ) Tj 27.360000 0.0 Td (waves ) Tj 28.560000 0.0 Td (with ) Tj ET BT 1.000000 0 0 1 50.520000 100.560000 Tm 3 Tr 0 0 0 rg /F0 10.200000 Tf 0.000000 0.0 Td (different ) Tj 40.920000 0.0 Td (wave ) Tj 25.680000 0.0 Td (phases. ) Tj 39.240000 0.0 Td (\177b ) Tj 11.160000 0.0 Td (is ) Tj 11.280000 0.0 Td (the ) Tj 18.120000 0.0 Td (phase ) Tj 28.920000 0.0 Td (angle ) Tj 27.600000 0.0 Td (\(rotating ) Tj ET BT 1.000000 0 0 1 50.400000 89.520000 Tm 3 Tr 0 0 0 rg /F0 10.440000 Tf 0.000000 0.0 Td (frame\) ) Tj 31.920000 0.0 Td (between ) Tj 38.880000 0.0 Td (the ) Tj 17.040000 0.0 Td (electron ) Tj 37.680000 0.0 Td (perpendicular ) Tj 63.000000 0.0 Td (velocity ) Tj 36.600000 0.0 Td (and ) Tj ET BT 1.000000 0 0 1 50.520000 79.200000 Tm 3 Tr 0 0 0 rg /F0 10.200000 Tf 0.000000 0.0 Td (the ) Tj 16.920000 0.0 Td (magnetic ) Tj 42.840000 0.0 Td (field ) Tj 21.600000 0.0 Td (vector ) Tj 29.880000 0.0 Td (of ) Tj 11.040000 0.0 Td (one ) Tj 18.000000 0.0 Td (of ) Tj 11.040000 0.0 Td (the ) Tj 16.800000 0.0 Td (waves, ) Tj 30.840000 0.0 Td (and ) Tj 18.960000 0.0 Td (a ) Tj 9.240000 0.0 Td (the ) Tj ET BT 1.000000 0 0 1 50.280000 68.760000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (pitch ) Tj 26.520000 0.0 Td (angle ) Tj 27.360000 0.0 Td (between ) Tj 39.960000 0.0 Td (the ) Tj 18.360000 0.0 Td (electron ) Tj 38.880000 0.0 Td (parallel ) Tj 36.360000 0.0 Td (velocity ) Tj 37.920000 0.0 Td (and ) Tj ET BT 1.000000 0 0 1 50.400000 58.320000 Tm 3 Tr 0 0 0 rg /F0 10.080000 Tf 0.000000 0.0 Td (the ) Tj 17.400000 0.0 Td (background ) Tj 54.600000 0.0 Td (magnetic ) Tj 43.080000 0.0 Td (field ) Tj 21.840000 0.0 Td (vector. ) Tj ET BT 1.000000 0 0 1 413.160000 743.760000 Tm 3 Tr 0 0 0 rg /F0 5.280000 Tf 0.000000 0.0 Td (BwlBo=O.001 ) Tj ET BT 1.000000 0 0 1 343.680000 719.040000 Tm 3 Tr 0 0 0 rg /F0 3.720000 Tf 0.000000 0.0 Td (0.1 ) Tj ET BT 1.000000 0 0 1 350.280000 573.480000 Tm 3 Tr 0 0 0 rg /F0 4.680000 Tf 0.000000 0.0 Td (-3 ) Tj 26.640000 0.0 Td (-2 ) Tj 26.520000 0.0 Td (-I ) Tj 29.280000 0.0 Td (0 ) Tj 26.760000 0.0 Td (I ) Tj 26.040000 0.0 Td (2 ) Tj 26.280000 0.0 Td (3 ) Tj ET BT 1.000000 0 0 1 415.920000 565.920000 Tm 3 Tr 0 0 0 rg /F0 6.480000 Tf 0.000000 0.0 Td (Phase ) Tj 19.920000 0.0 Td (Angle ) Tj ET BT 1.000000 0 0 1 304.080000 545.880000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (Figure ) Tj 37.440000 0.0 Td (2. ) Tj 14.520000 0.0 Td (For ) Tj 18.360000 0.0 Td (a ) Tj 8.520000 0.0 Td (w ) Tj 10.560000 0.0 Td (= ) Tj 11.160000 0.0 Td (fl/2, ) Tj 23.880000 0.0 Td (Bw ) Tj 17.880000 0.0 Td (= ) Tj 11.040000 0.0 Td (0.001Bo, ) Tj 41.040000 0.0 Td (the ) Tj 17.760000 0.0 Td (trajec- ) Tj ET BT 1.000000 0 0 1 303.960000 535.560000 Tm 3 Tr 0 0 0 rg /F0 9.960000 Tf 0.000000 0.0 Td (tories ) Tj 27.720000 0.0 Td (are ) Tj 16.800000 0.0 Td (regular ) Tj 34.080000 0.0 Td (for ) Tj 15.480000 0.0 Td (a ) Tj 8.160000 0.0 Td (particle ) Tj 36.480000 0.0 Td (of ) Tj 12.000000 0.0 Td (100 ) Tj 17.760000 0.0 Td (keV. ) Tj ET BT 1.000000 0 0 1 303.120000 507.360000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (where ) Tj 28.560000 0.0 Td (f] ) Tj 9.240000 0.0 Td (is ) Tj 9.720000 0.0 Td (equal ) Tj 26.160000 0.0 Td (to ) Tj 11.760000 0.0 Td (the ) Tj 16.680000 0.0 Td (parallel ) Tj 35.520000 0.0 Td (velocity ) Tj 36.480000 0.0 Td (near ) Tj 21.720000 0.0 Td (resonance. ) Tj ET BT 1.000000 0 0 1 303.120000 495.000000 Tm 3 Tr 0 0 0 rg /F0 10.440000 Tf 0.000000 0.0 Td (By ) Tj 17.640000 0.0 Td (substituting ) Tj 57.840000 0.0 Td (this ) Tj 21.120000 0.0 Td (value ) Tj 27.840000 0.0 Td (in ) Tj 14.280000 0.0 Td (\(9\) ) Tj 17.040000 0.0 Td (one ) Tj 19.920000 0.0 Td (finds ) Tj 25.680000 0.0 Td (that ) Tj 23.040000 0.0 Td (this ) Tj ET BT 1.000000 0 0 1 303.120000 483.000000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (equation ) Tj 42.240000 0.0 Td (is ) Tj 11.400000 0.0 Td (satisfied ) Tj 39.720000 0.0 Td (if ) Tj 11.040000 0.0 Td (\(3\) ) Tj 16.800000 0.0 Td (is ) Tj 11.160000 0.0 Td (obeyed ) Tj 34.920000 0.0 Td (and ) Tj 20.640000 0.0 Td (we ) Tj 15.600000 0.0 Td (shall ) Tj 24.480000 0.0 Td (see ) Tj ET BT 1.000000 0 0 1 303.120000 471.240000 Tm 3 Tr 0 0 0 rg /F0 9.840000 Tf 0.000000 0.0 Td (the ) Tj 17.040000 0.0 Td (resonances ) Tj 50.040000 0.0 Td (appear ) Tj 32.880000 0.0 Td (in ) Tj 11.520000 0.0 Td (the ) Tj 17.160000 0.0 Td (numerical ) Tj 45.840000 0.0 Td (solutions ) Tj 41.280000 0.0 Td (of ) Tj 11.040000 0.0 Td (the ) Tj ET BT 1.000000 0 0 1 303.120000 459.000000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (full ) Tj 17.760000 0.0 Td (equations ) Tj 45.600000 0.0 Td (of ) Tj 11.640000 0.0 Td (motion ) Tj 35.040000 0.0 Td (\(Figure ) Tj 35.520000 0.0 Td (2 ) Tj 8.280000 0.0 Td (onwards\). ) Tj 47.520000 0.0 Td (Equation ) Tj ET BT 1.000000 0 0 1 303.960000 446.640000 Tm 3 Tr 0 0 0 rg /F0 10.920000 Tf 0.000000 0.0 Td (\(9\) ) Tj 16.200000 0.0 Td (has ) Tj 18.720000 0.0 Td (resonances ) Tj 50.760000 0.0 Td (at ) Tj 13.080000 0.0 Td (\177b ) Tj 11.160000 0.0 Td (- ) Tj 11.760000 0.0 Td (0, ) Tj 12.000000 0.0 Td (n7r ) Tj 16.320000 0.0 Td (and ) Tj 20.160000 0.0 Td (at ) Tj 13.680000 0.0 Td (\(\177b- ) Tj 23.040000 0.0 Td (7\) ) Tj 13.920000 0.0 Td (- ) Tj 11.520000 0.0 Td (0, ) Tj ET BT 1.000000 0 0 1 303.240000 434.880000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (n7r. ) Tj 19.560000 0.0 Td (At ) Tj 14.280000 0.0 Td (these ) Tj 25.680000 0.0 Td (points ) Tj 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ET BT 1.000000 0 0 1 48.600000 537.240000 Tm 3 Tr 0 0 0 rg /F0 9.840000 Tf 0.000000 0.0 Td (particle ) Tj 36.600000 0.0 Td (energy ) Tj 32.400000 0.0 Td (remains ) Tj 37.560000 0.0 Td (constant. ) Tj ET BT 1.000000 0 0 1 50.400000 513.960000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (4. ) Tj 20.040000 0.0 Td (Conclusions ) Tj ET BT 1.000000 0 0 1 60.480000 492.720000 Tm 3 Tr 0 0 0 rg /F0 9.840000 Tf 0.000000 0.0 Td (It ) Tj 11.280000 0.0 Td (has ) Tj 18.480000 0.0 Td (been ) Tj 24.600000 0.0 Td (shown ) Tj 30.840000 0.0 Td (that ) Tj 22.440000 0.0 Td (coupling ) Tj 40.440000 0.0 Td (between ) Tj 38.880000 0.0 Td (two ) Tj 19.200000 0.0 Td (oppo- ) Tj ET BT 1.000000 0 0 1 50.280000 480.720000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (sitely ) Tj 25.920000 0.0 Td (propagating ) Tj 55.680000 0.0 Td (whistler ) Tj 37.440000 0.0 Td (mode ) Tj 26.400000 0.0 Td (waves ) Tj 27.480000 0.0 Td (of ) Tj 10.680000 0.0 Td (the ) Tj 16.560000 0.0 Td (same ) Tj 24.240000 0.0 Td (am- ) Tj ET BT 1.000000 0 0 1 50.280000 469.080000 Tm 3 Tr 0 0 0 rg /F0 9.480000 Tf 0.000000 0.0 Td (plitude ) Tj 33.960000 0.0 Td (and ) Tj 19.200000 0.0 Td (wavenumber ) Tj 57.600000 0.0 Td (can ) Tj 17.880000 0.0 Td (lead ) Tj 20.760000 0.0 Td (to ) Tj 11.760000 0.0 Td (stochastic ) Tj 45.480000 0.0 Td (electron ) Tj ET BT 1.000000 0 0 1 50.400000 456.960000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (dynamics. ) Tj 48.600000 0.0 Td (Specifically, ) Tj 53.640000 0.0 Td (it ) Tj 8.880000 0.0 Td (is ) Tj 9.240000 0.0 Td (shown ) Tj 29.280000 0.0 Td (that ) Tj 20.760000 0.0 Td (chaotic ) Tj 32.880000 0.0 Td (phenom- ) Tj ET BT 1.000000 0 0 1 50.280000 445.200000 Tm 3 Tr 0 0 0 rg /F0 9.360000 Tf 0.000000 0.0 Td (ena ) Tj 18.600000 0.0 Td (occur ) Tj 27.840000 0.0 Td (due ) Tj 19.200000 0.0 Td (to ) Tj 12.480000 0.0 Td (the ) Tj 17.520000 0.0 Td (presence ) Tj 40.440000 0.0 Td (of ) Tj 11.880000 0.0 Td (the ) Tj 17.280000 0.0 Td (second ) Tj 32.400000 0.0 Td (wave. ) Tj 28.800000 0.0 Td (For ) Tj ET BT 1.000000 0 0 1 50.280000 433.320000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (sufficiently ) Tj 50.760000 0.0 Td (small ) Tj 26.640000 0.0 Td (wave ) Tj 24.720000 0.0 Td (amplitudes, ) Tj 54.120000 0.0 Td (however, ) Tj 41.160000 0.0 Td (the ) Tj 17.280000 0.0 Td (devia- ) Tj ET BT 1.000000 0 0 1 50.160000 421.200000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (tions ) Tj 24.120000 0.0 Td (from ) Tj 23.760000 0.0 Td (the ) Tj 17.040000 0.0 Td (single ) Tj 27.600000 0.0 Td (whistler ) Tj 37.440000 0.0 Td (mode ) Tj 26.640000 0.0 Td (wave ) Tj 23.760000 0.0 Td (electron ) Tj 37.080000 0.0 Td (inter- ) Tj ET BT 1.000000 0 0 1 50.160000 409.080000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (actions ) Tj 34.080000 0.0 Td (is ) Tj 10.080000 0.0 Td (not ) Tj 18.000000 0.0 Td (significant ) Tj 47.760000 0.0 Td (and ) Tj 19.320000 0.0 Td (the ) Tj 17.160000 0.0 Td (motion ) Tj 33.600000 0.0 Td (of ) Tj 11.160000 0.0 Td (the ) Tj 17.040000 0.0 Td (particle ) Tj ET BT 1.000000 0 0 1 50.040000 397.320000 Tm 3 Tr 0 0 0 rg /F0 9.480000 Tf 0.000000 0.0 Td (in ) Tj 12.840000 0.0 Td (phase ) Tj 29.400000 0.0 Td (space ) Tj 28.320000 0.0 Td (can ) Tj 19.440000 0.0 Td (be ) Tj 14.880000 0.0 Td (considered ) Tj 50.280000 0.0 Td (as ) Tj 13.080000 0.0 Td (identical ) Tj 41.280000 0.0 Td (to ) Tj 13.200000 0.0 Td (that ) Tj ET BT 1.000000 0 0 1 50.040000 385.200000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (of ) Tj 11.880000 0.0 Td (a ) Tj 8.760000 0.0 Td (simple ) Tj 31.920000 0.0 Td (pendulum. ) Tj 52.440000 0.0 Td (As ) Tj 15.120000 0.0 Td (the ) Tj 17.760000 0.0 Td (amplitude ) Tj 47.280000 0.0 Td (increases ) Tj 42.000000 0.0 Td (the ) Tj ET BT 1.000000 0 0 1 50.160000 373.200000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (effects ) Tj 31.560000 0.0 Td (of ) Tj 12.720000 0.0 Td (the ) Tj 18.600000 0.0 Td (other ) Tj 27.480000 0.0 Td (wave ) Tj 25.560000 0.0 Td (on ) Tj 15.120000 0.0 Td (the ) Tj 18.360000 0.0 Td (particle ) Tj 36.960000 0.0 Td (by ) Tj 15.000000 0.0 Td (means ) Tj 31.560000 0.0 Td (of ) Tj ET BT 1.000000 0 0 1 50.040000 360.960000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (the ) Tj 18.960000 0.0 Td (Lorentz ) Tj 38.520000 0.0 Td (force ) Tj 25.920000 0.0 Td (become ) Tj 37.440000 0.0 Td (important, ) Tj 51.840000 0.0 Td (the ) Tj 18.720000 0.0 Td (integrals ) Tj 41.640000 0.0 Td (of ) Tj ET BT 1.000000 0 0 1 49.920000 349.080000 Tm 3 Tr 0 0 0 rg /F0 9.480000 Tf 0.000000 0.0 Td (motion ) Tj 34.320000 0.0 Td (are ) Tj 16.920000 0.0 Td (not ) Tj 18.120000 0.0 Td (conserved ) Tj 45.960000 0.0 Td (and ) Tj 19.440000 0.0 Td (regular ) Tj 33.840000 0.0 Td (dynamics ) Tj 44.040000 0.0 Td (can ) Tj 18.120000 0.0 Td (be ) Tj ET BT 1.000000 0 0 1 49.920000 337.440000 Tm 3 Tr 0 0 0 rg /F0 9.480000 Tf 0.000000 0.0 Td (maintained ) Tj 52.080000 0.0 Td (only ) Tj 21.720000 0.0 Td (in ) Tj 11.280000 0.0 Td (the ) Tj 16.920000 0.0 Td (vicinity ) Tj 35.400000 0.0 Td (of ) Tj 11.040000 0.0 Td (resonances; ) Tj 51.600000 0.0 Td (the ) Tj 16.920000 0.0 Td (KAM ) Tj ET BT 1.000000 0 0 1 50.160000 325.440000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (surfaces ) Tj 37.680000 0.0 Td (break ) Tj 27.840000 0.0 Td (up ) Tj 14.400000 0.0 Td (successively. ) Tj 57.720000 0.0 Td (It ) Tj 10.680000 0.0 Td (is ) Tj 9.960000 0.0 Td (also ) Tj 19.560000 0.0 Td (found ) Tj 27.720000 0.0 Td (that ) Tj 21.480000 0.0 Td (the ) Tj ET BT 1.000000 0 0 1 50.040000 313.200000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (value ) Tj 27.000000 0.0 Td (of ) Tj 12.360000 0.0 Td (the ) Tj 18.720000 0.0 Td (wave ) Tj 25.440000 0.0 Td (phase ) Tj 29.040000 0.0 Td (does ) Tj 23.640000 0.0 Td (not ) Tj 18.720000 0.0 Td (change ) Tj 33.720000 0.0 Td (the ) Tj 18.120000 0.0 Td (electron ) Tj ET BT 1.000000 0 0 1 50.160000 301.560000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (dynamics ) Tj 45.480000 0.0 Td (in ) Tj 13.080000 0.0 Td (a ) Tj 9.480000 0.0 Td (qualitative ) Tj 50.880000 0.0 Td (manner. ) Tj 43.560000 0.0 Td (Chaotic ) Tj 37.680000 0.0 Td (dynamics ) Tj ET BT 1.000000 0 0 1 50.040000 289.560000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (of ) Tj 11.280000 0.0 Td (electrons ) Tj 41.760000 0.0 Td (may ) Tj 21.720000 0.0 Td (allow ) Tj 25.680000 0.0 Td (significant ) Tj 47.400000 0.0 Td (pitch ) Tj 24.840000 0.0 Td (angle ) Tj 25.680000 0.0 Td (scattering ) Tj ET BT 1.000000 0 0 1 50.040000 277.440000 Tm 3 Tr 0 0 0 rg /F0 10.200000 Tf 0.000000 0.0 Td (into ) Tj 20.160000 0.0 Td (the ) Tj 17.280000 0.0 Td (loss ) Tj 18.960000 0.0 Td (cone ) Tj 23.400000 0.0 Td (\(phase ) Tj 31.080000 0.0 Td (space ) Tj 26.640000 0.0 Td (diffusion\) ) Tj 43.680000 0.0 Td (in ) Tj 11.280000 0.0 Td (the ) Tj 17.040000 0.0 Td (magne- ) Tj ET BT 1.000000 0 0 1 49.920000 265.560000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (tosphere ) Tj 41.040000 0.0 Td (under ) Tj 29.400000 0.0 Td (certain ) Tj 34.080000 0.0 Td (circumstances. ) Tj 69.360000 0.0 Td (Results ) Tj 35.640000 0.0 Td (suggest ) Tj ET BT 1.000000 0 0 1 49.920000 253.560000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (that ) Tj 21.960000 0.0 Td (for ) Tj 15.720000 0.0 Td (example ) Tj 39.720000 0.0 Td (for ) Tj 16.080000 0.0 Td (100 ) Tj 17.880000 0.0 Td (keV ) Tj 20.640000 0.0 Td (electrons, ) Tj 44.640000 0.0 Td (stochasticity ) Tj 57.720000 0.0 Td (is ) Tj ET BT 1.000000 0 0 1 50.040000 241.560000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (evident ) Tj 35.640000 0.0 Td (for ) Tj 16.080000 0.0 Td (wave ) Tj 25.080000 0.0 Td (amplitudes ) Tj 51.840000 0.0 Td (observed ) Tj 41.640000 0.0 Td (at ) Tj 12.480000 0.0 Td (L ) Tj 10.440000 0.0 Td (- ) Tj 10.920000 0.0 Td (6 ) Tj 8.640000 0.0 Td (during ) Tj ET BT 1.000000 0 0 1 50.160000 231.600000 Tm 3 Tr 0 0 0 rg /F0 7.560000 Tf 0.000000 0.0 Td (disturbed ) Tj 45.120000 0.0 Td (times. ) Tj ET BT 1.000000 0 0 1 61.320000 218.160000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (The ) Tj 19.920000 0.0 Td (diffusion ) Tj 39.840000 0.0 Td (coefficient ) Tj 45.840000 0.0 Td (for ) Tj 14.520000 0.0 Td (the ) Tj 16.320000 0.0 Td (process ) Tj 33.840000 0.0 Td (discussed ) Tj 42.240000 0.0 Td (here ) Tj ET BT 1.000000 0 0 1 51.120000 206.160000 Tm 3 Tr 0 0 0 rg /F0 9.480000 Tf 0.000000 0.0 Td (will ) Tj 19.680000 0.0 Td (be ) Tj 14.520000 0.0 Td (calculated ) Tj 48.360000 0.0 Td (in ) Tj 12.480000 0.0 Td (a ) Tj 8.880000 0.0 Td (future ) Tj 30.480000 0.0 Td (paper. ) Tj 33.960000 0.0 Td (However, ) Tj 43.680000 0.0 Td (we ) Tj 15.240000 0.0 Td (an- ) Tj ET BT 1.000000 0 0 1 51.240000 193.800000 Tm 3 Tr 0 0 0 rg /F0 10.200000 Tf 0.000000 0.0 Td (ticipate ) Tj 36.240000 0.0 Td (that ) Tj 21.840000 0.0 Td (pitch ) Tj 25.440000 0.0 Td (angle ) Tj 26.040000 0.0 Td (diffusion ) Tj 40.080000 0.0 Td (will ) Tj 18.600000 0.0 Td (scale ) Tj 23.760000 0.0 Td (as ) Tj 11.760000 0.0 Td (the ) Tj 17.040000 0.0 Td (local ) Tj ET BT 1.000000 0 0 1 51.240000 181.680000 Tm 3 Tr 0 0 0 rg /F0 10.080000 Tf 0.000000 0.0 Td (gyrofrequency. ) Tj 71.880000 0.0 Td (This ) Tj 24.120000 0.0 Td (is ) Tj 11.280000 0.0 Td (to ) Tj 13.440000 0.0 Td (be ) Tj 15.000000 0.0 Td (compared ) Tj 46.440000 0.0 Td (with ) Tj 24.000000 0.0 Td (stochas- ) Tj ET BT 1.000000 0 0 1 312.720000 741.000000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (Acknowledgments. ) Tj 97.320000 0.0 Td (This ) Tj 21.840000 0.0 Td (work ) Tj 23.400000 0.0 Td (was ) Tj 18.720000 0.0 Td (conducted ) Tj 44.880000 0.0 Td (whilst ) Tj ET BT 1.000000 0 0 1 302.880000 731.040000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (S.K.Matsoukis ) Tj 61.800000 0.0 Td (was ) Tj 18.120000 0.0 Td (partially ) Tj 37.440000 0.0 Td (supported ) Tj 43.440000 0.0 Td (by ) Tj 13.080000 0.0 Td (PPARC. ) Tj ET BT 1.000000 0 0 1 303.240000 703.800000 Tm 3 Tr 0 0 0 rg /F0 9.120000 Tf 0.000000 0.0 Td (References ) Tj ET BT 1.000000 0 0 1 303.480000 681.000000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Chapman,S.C., ) Tj 63.720000 0.0 Td (and ) Tj 16.800000 0.0 Td (Watkins,N.W.,Parametarization ) Tj 131.760000 0.0 Td (of ) Tj 9.600000 0.0 Td (chao ) Tj ET BT 1.000000 0 0 1 312.120000 670.920000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (tic ) Tj 13.320000 0.0 Td (particle ) Tj 33.720000 0.0 Td (dynamics ) Tj 40.920000 0.0 Td (in ) Tj 10.800000 0.0 Td (a ) Tj 7.440000 0.0 Td (simple ) Tj 28.800000 0.0 Td (time-dependant ) Tj 65.760000 0.0 Td (field ) Tj 19.800000 0.0 Td (re- ) Tj ET BT 1.000000 0 0 1 312.360000 660.960000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (versal ) Tj 23.640000 0.0 Td (,J. ) Tj 9.600000 0.0 Td (G ) Tj 7.080000 0.0 Td (eop ) Tj 14.160000 0.0 Td (hys. ) Tj 16.200000 0.0 Td (Res. ) Tj 17.640000 0.0 Td (,98,165,1993. ) Tj ET BT 1.000000 0 0 1 303.360000 650.520000 Tm 3 Tr 0 0 0 rg /F0 9.360000 Tf 0.000000 0.0 Td (Chen,J.,Nonlinear ) Tj 75.360000 0.0 Td (Dynamics ) Tj 41.880000 0.0 Td (of ) Tj 10.080000 0.0 Td (Charged ) Tj 35.760000 0.0 Td (Particles ) Tj 36.720000 0.0 Td (in ) Tj 9.840000 0.0 Td (te ) Tj 10.080000 0.0 Td (Mag- ) Tj ET BT 1.000000 0 0 1 312.360000 641.160000 Tm 3 Tr 0 0 0 rg /F0 8.400000 Tf 0.000000 0.0 Td (netotail, ) Tj ET BT 1.000000 0 0 1 312.240000 630.960000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (J. ) Tj 7.320000 0.0 Td (Geophys. ) Tj 37.440000 0.0 Td (Res. ) Tj 17.760000 0.0 Td (,97,15011,1992. ) Tj ET BT 1.000000 0 0 1 303.000000 621.000000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (Devine,P.E., ) Tj 53.520000 0.0 Td (and ) Tj 18.360000 0.0 Td (Chapman,S.C.,Selfconsistent ) Tj 118.440000 0.0 Td (simulation ) Tj ET BT 1.000000 0 0 1 312.000000 610.920000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (studies ) Tj 31.320000 0.0 Td (of ) Tj 10.800000 0.0 Td (nonlinear ) Tj 41.160000 0.0 Td (electron ) Tj 35.040000 0.0 Td (whistler ) Tj 35.040000 0.0 Td (wave ) Tj 23.040000 0.0 Td (particle ) Tj 33.120000 0.0 Td (inter- ) Tj ET BT 1.000000 0 0 1 312.240000 601.080000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (actions,Physica ) Tj 65.520000 0.0 Td (D.,95,35,1996. ) Tj ET BT 1.000000 0 0 1 303.000000 590.880000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Dysthe,K.B.,Some ) Tj 79.080000 0.0 Td (studies ) Tj 32.640000 0.0 Td (of ) Tj 11.880000 0.0 Td (triggered ) Tj 40.200000 0.0 Td (whistler ) Tj 36.480000 0.0 Td (emissions, ) Tj ET BT 1.000000 0 0 1 312.240000 581.040000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (J.Geophys. ) Tj 44.640000 0.0 Td (Res., ) Tj ET BT 1.000000 0 0 1 312.360000 571.080000 Tm 3 Tr 0 0 0 rg /F0 8.520000 Tf 0.000000 0.0 Td (76,6915,1971. ) Tj ET BT 1.000000 0 0 1 303.120000 560.880000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Faith ) Tj 24.240000 0.0 Td (J.,Electron ) Tj 47.760000 0.0 Td (precipitation ) Tj 54.720000 0.0 Td (caused ) Tj 29.880000 0.0 Td (by ) Tj 12.960000 0.0 Td (chaotic ) Tj 31.560000 0.0 Td (motion ) Tj 31.560000 0.0 Td (in ) Tj ET BT 1.000000 0 0 1 312.000000 550.680000 Tm 3 Tr 0 0 0 rg /F0 9.240000 Tf 0.000000 0.0 Td (the ) Tj 15.360000 0.0 Td (magnetosphere ) Tj 63.480000 0.0 Td (due ) Tj 16.920000 0.0 Td (to ) Tj 10.800000 0.0 Td (large ) Tj 22.200000 0.0 Td (amplitude ) Tj 42.480000 0.0 Td (whistler ) Tj 34.320000 0.0 Td (waves, ) Tj ET BT 1.000000 0 0 1 312.120000 540.960000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (J. ) Tj 10.560000 0.0 Td (Geophys. ) Tj 37.320000 0.0 Td (Res.,102,2233,1997. ) Tj ET BT 1.000000 0 0 1 303.120000 530.760000 Tm 3 Tr 0 0 0 rg /F0 9.240000 Tf 0.000000 0.0 Td (Gendrin, ) Tj 37.920000 0.0 Td (R., ) Tj 15.120000 0.0 Td (Phase-bunching ) Tj 66.480000 0.0 Td (and ) Tj 17.400000 0.0 Td (other ) Tj 23.400000 0.0 Td (non-linear ) Tj 43.080000 0.0 Td (processes ) Tj ET BT 1.000000 0 0 1 312.000000 520.920000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (occurring ) Tj 42.240000 0.0 Td (in ) Tj 12.120000 0.0 Td (Gyroresonant ) Tj 58.560000 0.0 Td (Wave ) Tj 26.160000 0.0 Td (Particle ) Tj 35.040000 0.0 Td (Interac- ) Tj 35.040000 0.0 Td (tions, ) Tj ET BT 1.000000 0 0 1 312.240000 511.080000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (Astrophys. ) Tj 47.880000 0.0 Td (and ) Tj 18.480000 0.0 Td (Space ) Tj 26.400000 0.0 Td (Sci.,28,245,1974. ) Tj ET BT 1.000000 0 0 1 302.880000 500.880000 Tm 3 Tr 0 0 0 rg /F0 9.120000 Tf 0.000000 0.0 Td (Kennel,C.F., ) Tj 56.280000 0.0 Td (and ) Tj 19.320000 0.0 Td (H.E. ) Tj 22.800000 0.0 Td (Petscheck,Limit ) Tj 68.040000 0.0 Td (on ) Tj 13.920000 0.0 Td (stably ) Tj 28.440000 0.0 Td (trapped ) Tj ET BT 1.000000 0 0 1 312.120000 491.040000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (particle ) Tj 33.480000 0.0 Td (fluxes, ) Tj 29.160000 0.0 Td (J.Geophys. ) Tj 48.960000 0.0 Td (Res., ) Tj 22.920000 0.0 Td (71, ) Tj 15.000000 0.0 Td (1, ) Tj 10.200000 0.0 Td (1966. ) Tj ET BT 1.000000 0 0 1 302.760000 480.960000 Tm 3 Tr 0 0 0 rg /F0 9.120000 Tf 0.000000 0.0 Td (Inan,U.S., ) Tj 46.320000 0.0 Td (Gyroresonant ) Tj 59.760000 0.0 Td (pitch ) Tj 25.320000 0.0 Td (angle ) Tj 25.560000 0.0 Td (scattering ) Tj 44.400000 0.0 Td (by ) Tj 14.520000 0.0 Td (coher- ) Tj ET BT 1.000000 0 0 1 311.880000 470.880000 Tm 3 Tr 0 0 0 rg /F0 9.120000 Tf 0.000000 0.0 Td (ent ) Tj 16.080000 0.0 Td (and ) Tj 18.240000 0.0 Td (incoherent ) Tj 45.600000 0.0 Td (whistler ) Tj 35.400000 0.0 Td (wave ) Tj 22.920000 0.0 Td (modes ) Tj 28.680000 0.0 Td (in ) Tj 10.920000 0.0 Td (the ) Tj 16.080000 0.0 Td (magneto- ) Tj ET BT 1.000000 0 0 1 311.880000 461.280000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (sp ) Tj 8.880000 0.0 Td (h ) Tj 5.160000 0.0 Td (ere,J. ) Tj 22.200000 0.0 Td (Geop ) Tj 21.120000 0.0 Td (hys. ) Tj 16.080000 0.0 Td (Res. ) Tj 17.760000 0.0 Td (,92,127,1987. ) Tj ET BT 1.000000 0 0 1 302.880000 451.200000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (Lyons,L.R. ) Tj 49.680000 0.0 Td (and ) Tj 20.280000 0.0 Td (Williams, ) Tj 44.760000 0.0 Td (D.J., ) Tj 25.680000 0.0 Td (Quantitative ) Tj 56.040000 0.0 Td (Aspects ) Tj 36.480000 0.0 Td (of ) Tj ET BT 1.000000 0 0 1 312.120000 441.000000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (Magnetospheric ) Tj 66.120000 0.0 Td (Physics, ) Tj 35.040000 0.0 Td (D. ) Tj 11.760000 0.0 Td (Reidel, ) Tj 30.000000 0.0 Td (Hingham, ) Tj 41.760000 0.0 Td (Mass., ) Tj 27.840000 0.0 Td (1984. ) Tj ET BT 1.000000 0 0 1 302.640000 431.040000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (Nagano, ) Tj 36.840000 0.0 Td (I.,Yagitani, ) Tj 48.840000 0.0 Td (S., ) Tj 13.800000 0.0 Td (Hirotsugu, ) Tj 46.080000 0.0 Td (K. ) Tj 13.080000 0.0 Td (and ) Tj 18.120000 0.0 Td (Matsumoto, ) Tj 51.840000 0.0 Td (H., ) Tj ET BT 1.000000 0 0 1 312.120000 420.960000 Tm 3 Tr 0 0 0 rg /F0 9.120000 Tf 0.000000 0.0 Td (Analysis ) Tj 38.640000 0.0 Td (of ) Tj 12.000000 0.0 Td (Wave ) Tj 26.640000 0.0 Td (Normal ) Tj 35.040000 0.0 Td (and ) Tj 19.680000 0.0 Td (Poynting ) Tj 40.200000 0.0 Td (Vectors ) Tj 34.080000 0.0 Td (of ) Tj 12.000000 0.0 Td (the ) Tj ET BT 1.000000 0 0 1 312.120000 410.760000 Tm 3 Tr 0 0 0 rg /F0 9.360000 Tf 0.000000 0.0 Td (Chorus ) Tj 31.920000 0.0 Td (Emissions ) Tj 43.200000 0.0 Td (observed ) Tj 38.520000 0.0 Td (by ) Tj 13.080000 0.0 Td (GEOTAIL,J.Geomag. ) Tj ET BT 1.000000 0 0 1 312.120000 401.280000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Geoelect ) Tj 34.440000 0.0 Td (r., ) Tj 9.000000 0.0 Td (48,299-307,1996. ) Tj ET BT 1.000000 0 0 1 302.880000 391.200000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (Parrot,M. ) Tj 42.360000 0.0 Td (and ) Tj 17.760000 0.0 Td (Gaye,C.A., ) Tj 47.280000 0.0 Td (A ) Tj 9.120000 0.0 Td (statistical ) Tj 41.760000 0.0 Td (survey ) Tj 28.440000 0.0 Td (of ) Tj 10.080000 0.0 Td (ELF ) Tj 20.280000 0.0 Td (waves ) Tj ET BT 1.000000 0 0 1 311.880000 381.240000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (in ) Tj 9.960000 0.0 Td (geostationary ) Tj 57.120000 0.0 Td (orbit,Geophys. ) Tj 59.760000 0.0 Td (Res. ) Tj 16.920000 0.0 Td (Letters, ) Tj 33.480000 0.0 Td (23,2463-2466, ) Tj ET BT 1.000000 0 0 1 312.360000 373.200000 Tm 3 Tr 0 0 0 rg /F0 6.720000 Tf 0.000000 0.0 Td (1994. ) Tj ET BT 1.000000 0 0 1 302.880000 361.440000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (Ram, ) Tj 26.400000 0.0 Td (A.K., ) Tj 26.640000 0.0 Td (Bets, ) Tj 25.560000 0.0 Td (A.,Hamiltonian ) Tj 66.600000 0.0 Td (chaos ) Tj 26.040000 0.0 Td (in ) Tj 11.880000 0.0 Td (Wave ) Tj 26.280000 0.0 Td (Particle ) Tj ET BT 1.000000 0 0 1 311.880000 351.480000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (Interactions, ) Tj 54.120000 0.0 Td (Phys. ) Tj 26.400000 0.0 Td (of ) Tj 11.040000 0.0 Td (Space ) Tj 26.280000 0.0 Td (Plasmas, ) Tj 35.640000 0.0 Td (13,341,1993. ) Tj ET BT 1.000000 0 0 1 302.760000 341.400000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (Tabor,M.,Chaos ) Tj 68.760000 0.0 Td (and ) Tj 18.000000 0.0 Td (Integrability ) Tj 53.280000 0.0 Td (in ) Tj 10.560000 0.0 Td (nonlinear ) Tj 40.800000 0.0 Td (dynamics: ) Tj ET BT 1.000000 0 0 1 312.120000 331.320000 Tm 3 Tr 0 0 0 rg /F0 9.360000 Tf 0.000000 0.0 Td (An ) Tj 15.120000 0.0 Td (Introduction ) Tj 54.840000 0.0 Td (\(Jonh ) Tj 25.800000 0.0 Td (Wiley, ) Tj 28.800000 0.0 Td (New ) Tj 20.640000 0.0 Td (York, ) Tj 25.440000 0.0 Td (1989\). ) Tj ET BT 1.000000 0 0 1 302.760000 321.480000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Thorne ) Tj 32.640000 0.0 Td (R.M., ) Tj 26.640000 0.0 Td (and ) Tj 18.240000 0.0 Td (Horne,R.B., ) Tj 51.720000 0.0 Td (Landau ) Tj 33.600000 0.0 Td (damping ) Tj 37.800000 0.0 Td (of ) Tj 10.560000 0.0 Td (magne- ) Tj ET BT 1.000000 0 0 1 311.880000 311.640000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (tospherically ) Tj 53.760000 0.0 Td (reflected ) Tj 36.360000 0.0 Td (whistlers,J.Geo- ) Tj 66.840000 0.0 Td (phys. ) Tj 21.120000 0.0 Td (Res.,99,17249, ) Tj ET BT 1.000000 0 0 1 312.480000 303.240000 Tm 3 Tr 0 0 0 rg /F0 6.840000 Tf 0.000000 0.0 Td (1994. ) Tj ET BT 1.000000 0 0 1 302.760000 291.600000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Thorne,R.M., ) Tj 57.600000 0.0 Td (and ) Tj 17.160000 0.0 Td (Horne,R.B., ) Tj 50.400000 0.0 Td (Whistler ) Tj 37.080000 0.0 Td (absorption ) Tj 44.400000 0.0 Td (and ) Tj 16.800000 0.0 Td (elec- ) Tj ET BT 1.000000 0 0 1 311.880000 281.520000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (tron ) Tj 20.160000 0.0 Td (heating ) Tj 33.240000 0.0 Td (near ) Tj 20.760000 0.0 Td (the ) Tj 16.320000 0.0 Td (plasmapause,J.Geophys. ) Tj 97.800000 0.0 Td (Res.,101, ) Tj ET BT 1.000000 0 0 1 310.080000 270.600000 Tm 3 Tr 0 0 0 rg /F0 8.400000 Tf 0.000000 0.0 Td (4917, ) Tj 24.720000 0.0 Td (1996. ) Tj ET BT 1.000000 0 0 1 300.960000 260.640000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (VillaIon, ) Tj 36.720000 0.0 Td (E., ) Tj 14.040000 0.0 Td (Burke, ) Tj 28.920000 0.0 Td (W.J.,Rothwell,P.L., ) Tj 82.080000 0.0 Td (and ) Tj 17.160000 0.0 Td (Silevitch, ) Tj 39.120000 0.0 Td (M.B., ) Tj ET BT 1.000000 0 0 1 310.440000 250.800000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Quasi-linear ) Tj 52.440000 0.0 Td (wave ) Tj 23.280000 0.0 Td (particle ) Tj 33.840000 0.0 Td (interactions ) Tj 50.280000 0.0 Td (in ) Tj 11.040000 0.0 Td (the ) Tj 16.320000 0.0 Td (Earth's ) Tj 32.400000 0.0 Td (ra- ) Tj ET BT 1.000000 0 0 1 310.440000 240.840000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (diation ) Tj 31.320000 0.0 Td (belts,J.Geophys. ) Tj 66.840000 0.0 Td (Res., ) Tj 23.160000 0.0 Td (94, ) Tj 15.360000 0.0 Td (15243,1989a. ) Tj ET BT 1.000000 0 0 1 301.080000 230.640000 Tm 3 Tr 0 0 0 rg /F0 9.120000 Tf 0.000000 0.0 Td (VillaIon, ) Tj 39.240000 0.0 Td (E., ) Tj 16.680000 0.0 Td (Silevitch, ) Tj 42.120000 0.0 Td (M.B., ) Tj 27.600000 0.0 Td (Burke, ) Tj 31.200000 0.0 Td (W.J.,Rothwell, ) Tj 64.920000 0.0 Td (P.L., ) Tj ET BT 1.000000 0 0 1 310.440000 220.560000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (Gyroresonant ) Tj 59.400000 0.0 Td (interaction ) Tj 48.000000 0.0 Td (of ) Tj 12.000000 0.0 Td (energetic ) Tj 40.320000 0.0 Td (trapped ) Tj 35.760000 0.0 Td (electrons ) Tj ET BT 1.000000 0 0 1 310.320000 210.480000 Tm 3 Tr 0 0 0 rg /F0 9.480000 Tf 0.000000 0.0 Td (and ) Tj 17.520000 0.0 Td (protons, ) Tj 36.360000 0.0 Td (in ) Tj 10.680000 0.0 Td (Physics ) Tj 32.880000 0.0 Td (of ) Tj 10.560000 0.0 Td (Space ) Tj 25.680000 0.0 Td (Plasmas\(1989\),SPI ) Tj 78.720000 0.0 Td (Con. ) Tj ET BT 1.000000 0 0 1 310.440000 200.520000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (Proc. ) Tj 21.240000 0.0 Td (Reprint ) Tj 36.240000 0.0 Td (Set., ) Tj 22.920000 0.0 Td (vol.9,edited ) Tj 51.120000 0.0 Td (by ) Tj 14.160000 0.0 Td (T.Chang, ) Tj 43.320000 0.0 Td (G.B.Crew, ) Tj ET BT 1.000000 0 0 1 310.440000 190.440000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (and ) Tj 17.880000 0.0 Td (J.R. ) Tj 19.920000 0.0 Td (Jasperse,p.365, ) Tj 64.440000 0.0 Td (Scientific,Cambridge,Mass., ) Tj ET BT 1.000000 0 0 1 310.800000 181.800000 Tm 3 Tr 0 0 0 rg /F0 7.200000 Tf 0.000000 0.0 Td (1989b. ) Tj ET BT 1.000000 0 0 1 51.240000 170.040000 Tm 3 Tr 0 0 0 rg /F0 10.200000 Tf 0.000000 0.0 Td (tic ) Tj 14.880000 0.0 Td (diffusion ) Tj 41.160000 0.0 Td (due ) Tj 19.200000 0.0 Td (to ) Tj 12.600000 0.0 Td (bounce ) Tj 34.680000 0.0 Td (resonance ) Tj 46.440000 0.0 Td (\(e.g. ) Tj 23.280000 0.0 Td (Faith ) Tj 26.400000 0.0 Td (et ) Tj 11.880000 0.0 Td (al, ) Tj 19.200000 0.0 Td (Villalon,E. ) Tj 45.480000 0.0 Td (and ) Tj 17.040000 0.0 Td (Burke,W.J.,Near-Equatorial ) Tj 116.160000 0.0 Td (Pitch ) Tj 23.280000 0.0 Td (Angle ) Tj 25.320000 0.0 Td (Dif- ) Tj ET BT 1.000000 0 0 1 51.840000 157.560000 Tm 3 Tr 0 0 0 rg /F0 12.000000 Tf 0.000000 0.0 Td (1997\) ) Tj 26.760000 0.0 Td (of ) Tj 11.640000 0.0 Td (electrons ) Tj 42.240000 0.0 Td (with ) Tj 22.800000 0.0 Td (whistler ) Tj 38.040000 0.0 Td (mode ) Tj 26.760000 0.0 Td (waves ) Tj 28.080000 0.0 Td (which ) Tj 28.560000 0.0 Td (will ) Tj 33.600000 0.0 Td (fusion ) Tj 26.640000 0.0 Td (of ) Tj 10.560000 0.0 Td (Energetic ) Tj 41.400000 0.0 Td (Electrons ) Tj 40.560000 0.0 Td (by ) Tj 12.960000 0.0 Td (Oblique ) Tj 33.720000 0.0 Td (Whistler ) Tj 37.320000 0.0 Td (Waves, ) Tj ET BT 1.000000 0 0 1 51.480000 146.280000 Tm 3 Tr 0 0 0 rg /F0 12.840000 Tf 0.000000 0.0 Td (scale ) Tj 24.480000 0.0 Td (with ) Tj 23.280000 0.0 Td (the ) Tj 18.000000 0.0 Td (bounce ) Tj 34.680000 0.0 Td (frequency, ) Tj 48.120000 0.0 Td (this ) Tj 19.800000 0.0 Td (may ) Tj 21.960000 0.0 Td (be ) Tj 13.920000 0.0 Td (reflected ) Tj 54.720000 0.0 Td (J.Geophys. ) Tj 48.960000 0.0 Td (Res.,96,9655,1991. ) Tj ET BT 1.000000 0 0 1 51.360000 133.920000 Tm 3 Tr 0 0 0 rg /F0 9.960000 Tf 0.000000 0.0 Td (in ) Tj 11.040000 0.0 Td (the ) Tj 16.920000 0.0 Td (much ) Tj 26.520000 0.0 Td (larger ) Tj 28.200000 0.0 Td (wave ) Tj 24.120000 0.0 Td (amplitudes ) Tj 50.640000 0.0 Td (required ) Tj 38.520000 0.0 Td (in ) Tj 11.160000 0.0 Td (Faith ) Tj 25.440000 0.0 Td (et ) Tj ET BT 1.000000 0 0 1 310.560000 127.320000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (Space ) Tj 27.360000 0.0 Td (and ) Tj 19.800000 0.0 Td (Astrophysics ) Tj 56.280000 0.0 Td (Group, ) Tj 32.760000 0.0 Td (University ) Tj 45.720000 0.0 Td (of ) Tj 11.640000 0.0 Td (Warwick, ) Tj ET BT 1.000000 0 0 1 51.360000 118.920000 Tm 3 Tr 0 0 0 rg /F0 12.960000 Tf 0.000000 0.0 Td (al ) Tj 11.880000 0.0 Td (1997 ) Tj 23.040000 0.0 Td (for ) Tj 15.960000 0.0 Td (diffusion. ) Tj 44.880000 0.0 Td (Also, ) Tj 25.560000 0.0 Td (there ) Tj 25.800000 0.0 Td (is ) Tj 10.440000 0.0 Td (some ) Tj 24.960000 0.0 Td (evidence ) Tj 40.080000 0.0 Td (that ) Tj 27.120000 0.0 Td (UK ) Tj ET BT 1.000000 0 0 1 51.360000 110.040000 Tm 3 Tr 0 0 0 rg /F0 10.080000 Tf 0.000000 0.0 Td (this ) Tj 19.440000 0.0 Td (process ) Tj 35.280000 0.0 Td (will ) Tj 18.720000 0.0 Td (still ) Tj 19.200000 0.0 Td (occur ) Tj 26.880000 0.0 Td (when ) Tj 25.920000 0.0 Td (the ) Tj 16.920000 0.0 Td (fields ) Tj 25.200000 0.0 Td (and ) Tj 19.080000 0.0 Td (electron ) Tj ET BT 1.000000 0 0 1 51.480000 98.040000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (motion ) Tj 34.560000 0.0 Td (are ) Tj 17.160000 0.0 Td (evolved ) Tj 36.360000 0.0 Td (selfconsistently ) Tj 69.840000 0.0 Td (\(Devine ) Tj 36.840000 0.0 Td (and ) Tj 20.040000 0.0 Td (Chap- ) Tj 35.520000 0.0 Td (\(Received ) Tj 42.000000 0.0 Td (August ) Tj 32.760000 0.0 Td (25, ) Tj 15.120000 0.0 Td (1997; ) Tj 26.880000 0.0 Td (revised ) Tj 31.440000 0.0 Td (November ) Tj 43.680000 0.0 Td (6, ) Tj 10.440000 0.0 Td (1997; ) Tj ET BT 1.000000 0 0 1 51.360000 85.680000 Tm 3 Tr 0 0 0 rg /F0 12.360000 Tf 0.000000 0.0 Td (man, ) Tj 25.800000 0.0 Td (1996\). ) Tj 224.040000 0.0 Td (accepted ) Tj 38.040000 0.0 Td (November ) Tj 44.520000 0.0 Td (28, ) Tj 15.240000 0.0 Td (1997.\) ) Tj endstream endobj 16 0 obj <> endobj 17 0 obj <> endobj 18 0 obj <> stream application/pdf Space Plasma Physics: Wave/particle interactions; Mathematical Geophysics: Chaos; Magnetospheric Physics: Magnetosphere&mdash;inner Whistler mode wave coupling effects on electron dynamics in the near Earth magnetosphere S. K. Matsoukis, S. Chapman, G. Rowlands http://dx.doi.org/10.1029/97GL03716, doi:10.1029/97GL03716 escape 1.1 2007-01-05T14:19:01Z www.PrincetonImaging.com 2012-07-18T14:16-04:00 2012-07-18T14:16-04:00 uuid:94b2f92f-ad32-4f1a-9b17-9c4a39f9f732 uuid:b6531b79-6f6f-4f1e-bfc8-ea89a7ae9d1b endstream endobj xref 0 19 0000000000 65535 f 0000087735 00000 n 0000087930 00000 n 0000172919 00000 n 0000172949 00000 n 0000173034 00000 n 0000200000 00000 n 0000200195 00000 n 0000330070 00000 n 0000330101 00000 n 0000330186 00000 n 0000354451 00000 n 0000354649 00000 n 0000457923 00000 n 0000457956 00000 n 0000458042 00000 n 0000486173 00000 n 0000486249 00000 n 0000486890 00000 n trailer << /Size 19 >> startxref 160 %%EOF